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I'm no mathematician, but shouldn't the definition of Mersenne prime include that it has to be one less than an natural power of two? Also, in the chart of Mersenne primes, shouln't the first entry be 2^0 - 1, which is 0?
No. 0 is not a prime number. It's divisible by every other integer-- 129.15.228.164 22:48, 3 September 2006 (UTC)
It is easy to see that 2p-1 is prime iff p is prime... I'm not sure its really easy at all... maybe I'll wait for the proof to come up on the Prime numberss page; but in the mean time, the sentence should be reworded for a regular guy (like me) to know whats going on. --cM
It is not hard. If p is not prime, then you can write p as qr. It is easy to see that 2^q-1 and 2^r-1 are then divisors of 2^p-1 and therefore 2^p-1 is not prime either. The reason is obvious if you write 2^p-1 in the binary form. It looks like the digit "1" repeated p times (1111...). Similarly, 2^q-1 is the number 1 repeated q times. For example, 2^15-1 is 111111111111111, and 2^3-1 is 111, and the latter is obviously a divisor of the former because the ratio is 1001001001001. See also my text at the bottom. -- Lumidek 14:04, 6 Jun 2004 (UTC)
Ok, I'll reword it. In fact, "iff" is wrong. If 2p-1 is prime, then p must itself be prime.
--Axel
"Iff" being the abbreviation used in logic for "if and only if"?
Yes.
Generally, it seems to me bad form to ever use the words "clearly", "it is easy to see", and similar in math articles here. These are assuming a certain audience. Even if something is really, really clear, it's probably best not to use this. There will be someone learning it for the first time (we all learned "clear" things a first time) and "clearly" or "easy" may be off-putting. Revolver 04:57, 8 Jun 2004 (UTC)
2^31 - 1 = 2,147,483,647 !? Isnt that a prime? (see Two_billion_one_hundred_forty-seven_million_four_hundred_eighty-three_thousand_six_hundred_forty-seven, alas it will probably be deleted soon :b!) // Noone
What exactly is a "Mersenne number"? I've seen three different difinitions as of late. Obviously to be a candidate for a Mersenne prime a number must be "one less than a prime power of two", but isn't a "Mersenne number" simply "one less than a power of two"? -- Pascal666 05:02, 6 Jun 2004 (UTC)
After some exhaustive googling, I managed to fix all the links to point to articles using each mathematician's full name. However, I was completely unable to find "R.E. Powers"'s full name. Does anyone happen to know it?
The text says 'before 1461'. The table says 1456. Which is it?
If M(n)=2^n-1, is there a sequence n,M(n),M(M(n)),...,M(M(...M(n)...)) (k is the length of the sequence) where all the numbers are prime? What are the values of n for different values of k? Is there such a sequence for all k?
One source I read had Codice Palatino as the discoverer of M13 in 573. Another source had Cataldi as the first to prove the primality in 1588. The table has 1456 as the date of discovery of M13... but the table has no discoverer. This is why I believe that the table is the least credible of the 3... The other two have not only a date of discovery, but also a discoverer.
I have reverted a suspicious edit [3] by 202.163.246.145 claiming that M32 was found on April 1 instead of February 19 and M33 on February 1 instead of January 10. The contributor did not offer any justification for the change and all sources I checked (e.g. [4]) confirm the original dates. So I believe the edit has been just a vandalism/test. -- Mormegil 10:57, 16 July 2005 (UTC)
On December 16th, the 43rd known Mersenne prime was announced. If you can't live without a guess, it could be, among other choices, M 30402457, found by Curtis Cooper, but because you have no reason to believe my random generator, there is no reason for you to propagate the hypothesis. ;-) -- Lumidek 04:38, 21 December 2005 (UTC)
According to the
Gimps Status page, all exponents up to 15,300,000 have been
Lucas-Lehmer tested at least once. This definitely confirms that M13,466,917 is the 39th Mersenne prime.
—
Herbee
20:55, 4 January 2006 (UTC)
Qutezuce, do you know the unit for the countdown: days ? exponents ? --FvdP 21:13, 5 January 2006 (UTC) (I guess exponents --FvdP 21:24, 5 January 2006 (UTC))
Your guess would be correct. To quote the site http://www.mersenne.org/status.htm:
July 10, 2006: Double-checking proves M(13466917) is the 39th Mersenne prime.
April 23, 2007: All exponents below 15,000,000 double-checked.
From the foregoing it appears that exponents are being double-checked at the rate of about a million every six months.
So M(20996011) may not be confirmed as the 40th until Spring 2010 unless exponents are double-checked more quickly.
Glenn L 09:23, 2 July 2007 (UTC)
There is an IP address that is making some changes to the credit for M32. I believe this table is based on the database at primes.utm.edu, more specifically this page. That page credits Slowinski and Gage with M32. The IP address claims to be involved in this find, and said that they decided to credit only Harwell because it was his machine. However I believe primes.utm.edu uses a different criteria to give credit. For example the most recent of the Mersenne primes found by GIMPS was found on a computer owned by a university, but they gave credit to the people who administered the program to run the prime-checking software on hundreds of machines across the campus. So for now I've reverted the change, but I hope that the IP address returns and we can discuss this futher on this talk page. Qutezuce 20:31, 30 January 2006 (UTC)
Yes, This is my exact point; Slowinski and Gage had nothing to do with this find apart from supplying the code to me. I installed the code on the Cray-2 in a modified way, allowing to be run only when the system was completely idle. I found the M32 exponant and imediately passed it on to David and Paul for verification. Subsequently Harwell was given credit for the find as it was their machine. Perhaps George Woltman should be given credit for all of the subsequent finds !. 09:20 GMT 3rd Feb 2006
As a follow up to this discussion, http://primes.utm.edu/notes/756839.html has been created, and http://primes.utm.edu/mersenne/index.html has been updated with the credits - et al. 13:47 20th Feb 2006 (GMT)
The correct notation is "Mersenne 32", not M32... In fact, M32 is not even prime because 32 is composite. —Preceding unsigned comment added by PhiEaglesfan712 ( talk • contribs)
Could someone please explain, possibly in the article, just how the naming convention works for these things? I mean, where does the choice of the number in the subscript come from, as in the 13 in M13, for example? Narxysus 07:56, 7 May 2006 (UTC)
The very beginning of the main article defines the convention:
However, M13 should not be confused with M13:
Glenn L 06:36, 9 July 2007 (UTC)
You guys are still using the notation the wrong way...
M13 = 213 - 1 = 8191 is "Mersenne 5" not M5
M5 = 25 - 1 = 31, which in fact is "Mersenne 3"
Mersenne 13 is M521 = 2521 - 1 (≈ 6.8648 × 10156). —The preceding unsigned comment was added by PhiEaglesfan712 ( talk • contribs).
"On September 4, 2006, a computer reported finding the 44th known Mersenne prime. Verification will begin shortly, probably taking a week or so to complete. If it is verified, this will be GIMPS' tenth prime!" http://www.mersenne.org/prime.htm
NevilleDNZ 23:34, 4 September 2006 (UTC)
Could someone please explain (and add to the article) what Mersenne primes are useful for / why they are of any interest. Is it just because of their extraordinary size? Can you do stuff (not just pure arithmetics) with Mersenne primes that you can't do with other primes?
I saw the call for a citation following the statement of how many pages would be required to print M44. So I fired up Microsoft Word 2003, imported the text of M44 (downloaded from www.mersenne.org), set the margins to one inch and the typeface to 12-point Times New Roman, and voila: two thousand and seven hundred and thirty and four pages (to be precise, 2,733 full pages each containing 46 lines of 78 digits, plus a partial page containing 30 full lines and a partial line containing 14 digits). This result differs slightly from the number of pages indicated by Jmalc, which I attribute to slight differences in line spacing between Jmalc's word processor and mine.
Unfortunately, this constitutes original research and thus is not usable here. My chances of getting this fact published in a reputable journal is small (at best), so there will be no citation. Too bad. Jmalc's result is also original research. Perhaps, under the new policies, this whole statement should be purged. — SWWright Talk 20:12, 16 April 2007 (UTC)
Not sure if this section should even be part of the article in the first place but it's not hard to see the current info is wrong since by the most significant digits in the factors (5 and 2), the most significant digit in the product should thus be a 1 instead of a 5. Not sure if the value or the factors are wrong....can someone verify? Sentri 01:42, 23 May 2007 (UTC)
Oh nvm...my bad...didn't see the first factor Sentri 01:43, 23 May 2007 (UTC)
I think codice is the plural of codex. Kope 05:21, 14 June 2007 (UTC)
This isn't true if one of x or y is zero, or if x=y. However, outside of those degenerate cases, I'm not entirely sure that x^a-y^a|x^b-y^b implies a|b (of course, the proof of the converse is straightforward). 192.236.44.130 07:30, 12 August 2007 (UTC)
PhiEaglesfan712 has changed the definition of Mersenne number and posted in an old section. See section 2 #Mersenne number for discussion. PrimeHunter 02:08, 15 August 2007 (UTC)
I have moved the discussion here. Arcfrk 02:17, 20 August 2007 (UTC)
I strongly suggest you discuss on talk pages before changing definitions of article subjects that require significant changes to the article text and other articles, as you did in Mersenne number [7] and Double Mersenne number [8]. And using edit summary "fix definition of Double Mersenne number - with source" [9] followed by deletion of a link to a reliable and popular source that uses the former definition [10] is misleading. In addition, it's unclear whether your source here [11] actually requires prime exponent in Mersenne numbers. The glossary at the same site, http://primes.utm.edu/glossary/page.php?sort=MersenneNumber, does not require prime exponent but just says that many authors do.
Fermat numbers are of form 2^(2^n)+1 and Fermat primes are prime Fermat numbers. 2 = 2^0+1 cannot be written as 2^(2^n)+1, so it's not a Fermat number and therefore not a Fermat prime. I don't see any reason why this should affect the definition of Mersenne numbers. And Wikipedia definitions should be based on reliable sources and not on what "makes sense" to an editor making original research analogies. Reliable sources use two different definitions so we should say both are in use and not delete one of them like you did. For practical reasons we either have to choose one of them in our articles, or write two versions of many things which would be an unnecessary mess. I recommend we choose 2^n-1 for integer n and not restricted to prime n. It's common, for example in http://mathworld.wolfram.com/MersenneNumber.html. It's practical to use the more general definition when writing things that are relevant for both versions. Other articles, for example Repunit#Generalizations, would require changes if we change to PhiEaglesfan712's definition (and Mersenne number would require further changes). Many things depend on a common definition we have used for a long time and we should not change it without very good reason. PrimeHunter 23:46, 14 August 2007 (UTC)
Paulo Ribenboim, The Book of Prime Number Records, 2nd edition, Chapter 2, Section VII Mersenne Numbers, says 'The numbers (with q prime) are called Mersenne numbers'. DRLB 17:19, 20 August 2007 (UTC)
I have rewritten the lead, trying to make it less terse and more readable. I have also restored the old definition of the Mersenne number. One of the most authoritative sources on the subject, Crandall and Pomerance, define the "Mersenne numbers" to be the numbers of the form
They are using a diffirent letter as a mnemonic devise to indicate that we are mostly interested in these numbers for certain special values of q, but the definition is worded for arbitrary natural exponent q. A footnote with an explantion of conventions may be added, but I felt reluctant to put it into the lead. Alternatively, an explanation can be given later in the main text. PrimeHunter gave above a compelling consistency argument for keeping the present convention.
Other changes to the lead: streamlined typography (hopefully, correct and consistent); removed clutter; added a brief mention of Lucas–Lehmer test; moved repunit property closer to the definition of Mersenne numbers, in order not to break the continuity of the exposition of Mersenne primes. Arcfrk 02:26, 20 August 2007 (UTC)
At the bottom of the List of Known Mersenne Primes section, a statistic is given that it would take 2769 pages to display M44 in a standard word processor, and then it's marked as "Citation Needed". Unfortunately, an exact figure (and by extension, the validity of any citation) may be impossible, as this number will vary a little bit, since some word processors and some printers will alter the space between characters or lines ever so slightly (as well as several other less-critical factors).
However, since we know the number of digits in M44, and numbers are usually fixed-width, even in proportionally-spaced fonts, it's easy enough to attempt to duplicate the statistic with a simple macro. Using Microsoft Word XP for the PC, I got 2734 pages using all 0's. This certainly seems to be in line with the original poster's comment, though not exactly the same for the various reasons just noted. -- Rob 22:17, 15 September 2007 (UTC)
This strikes me as a tad pompous:
Perhaps even more embarrassingly, it is not known whether infinitely many Mersenne numbers with prime exponents are composite
Could this be reworded to avoid the implication that Wikipedia is ashamed of mathematicians who can't prove a property so painfully simple, when most of humanity can't even understand what that property is? -- Doradus 02:51, 22 September 2007 (UTC)
This states that xa − ya | xb − yb if and only if a|b —Preceding unsigned comment added by Barneypitt ( talk • contribs) 22:57, 18 January 2008 (UTC)
Thanks all for fascinating article, I would appreciate a x-reference next to the statement...
This states that xa − ya | xb − yb if and only if a|b
under the "Searching for Mersenne primes" section. If anyone would like to let me know how I add a "reference required" comment instead of using the chat page then thanks (sorry, newbie).
Thanks again, B —Preceding unsigned comment added by Barneypitt ( talk • contribs) 23:02, 18 January 2008 (UTC)
Shouldn't the article explain who Mersenne was? A bit lower down, the article says that Euclid worked on them, so how did the Mersenne number/prime come to be named after Mersenne? AnteaterZot ( talk) 12:00, 14 March 2008 (UTC)
I was reading a book in which Mersenne Numbers and prime numbers where referred in a way it made me confuse, so I came to Wikipedia for clarify my doubts, only to find that this article confused me too. It was only after re-reading and checking the discussion page that I finally concluded that not all Mersenne numbers are prime numbers too.
So, I ask: Why not making an exclusive article for Mersenne numbers instead of redirecting it to the article of Mersenne primes?
-- Francisco Albani ( talk) 00:54, 24 March 2008 (UTC)
I have removed a new section called "Distribution of Mersenne primes" with this text:
p is the exponent in a Mersenne prime. The conjecture appears non-notable and I see no good reason to believe it. The conjecture was clearly made to fit 4 known data points: There is 1 Mersenne prime exponent p with 2^1 < p < 2^2, there are 3 with 2^2 < p < 2^4, there are 7 with 2^4 < p < 2^8, and there are 15 with 2^8 < p < 2^16. The conjecture then predicts 31 with 2^16 < p < 2^32. This may take decades to test. I guess the conjecture was made after experimenting with a lot of guesses involving different sets of data points. Given the law of small numbers, there is likely to be a small data set which matches some pattern by "coincidence", without following the pattern forever. If a good independent source is found then the conjecture might be mentioned in Mersenne conjectures. PrimeHunter ( talk) 13:19, 27 April 2008 (UTC)
play in the article. Although MathWorld and Wikipedia define them as all numbers of form (2^n - 1), Sloanes Handbook of integer sequences leans towards requiring n to be prime. A couple sentences about what number theory texts prefer would be good. Rich ( talk) 09:43, 13 May 2008 (UTC)
The article currently says "Mersenne gave no indication how he came up with his list..." This contradicts Dickson, History of the Theory of Numbers, I, 13 and note 61, who lists the criteria by which Mersenne selected his numbers. In 1647 Mersenne stated without proof that Mp is prime when p is a prime of one of the three forms 4m + 1, 4m + 3, or 2m - 1 (the last, namely itself a Mersenne prime, being somewhat obscurely expressed by Mersenne). Applying this test to all Mersenne numbers below M8191 yields exactly Mersenne's four picks, namely M31, M67, M127, and M257.
So in the range Mersenne considered, his first two rules, yielding M67 and M257, scored 0% while his recursive rule, that Mp is a Mersenne prime when p is, yielding M31 and M127, scored 100%. Though the first two rules served him poorly, thanks to the third rule he ended up with a better overall score than he could have expected had he simply picked four primes at random between 19 and 257.
So while it's true that Mersenne gave no indication how he came up with his rules, that's not to say that he gave no indication how he came up with his list. If there are no objections by the end of the month I suggest adjusting the article accordingly. -- Vaughan Pratt ( talk) 04:16, 14 May 2008 (UTC)
Someone needs to make the above change in the text. Additionally, if Mersenne published M31 and M127 in 1647, why does the table attribute their discoveries to others a century or two later (M31 by Euler in 1772 and M127 by Lucas in 1876). Is Mersenne not given credit because his was only a conjecture and not a proof? If so, that should be explicitely stated somewhere. 68.73.93.0 ( talk) 07:32, 27 September 2008 (UTC)
Yes he's not given credit because he didn't prove it. Nico92400 ( talk) 08:03, 29 September 2008 (UTC)
I understand that a "Mersenne number is a number that is one less than a power of two". However, why do these numbers warrant a special name? what is their significance? -- Sreifa01 ( talk) 12:28, 26 May 2008 (UTC)
(copied from talk:Prime_number) There's little more besides a headline stating more information to come soon, but http://mersenne.org/prime.htm claims to possibly have found the 45th mersenne prime number. Slashdot has also covered it. -- 76.85.144.126 ( talk) 00:32, 28 August 2008 (UTC)
On Saturday, GIMPS found one more, 46th Mersenne prime. ;-) [18] The exponent is probably around 40 million, too. It will take two weeks or so to check it. -- Lumidek ( talk) 07:08, 8 September 2008 (UTC)
Peoples, peoples, peoples - stop fighting over 44 in August versus 46 in September. The two new ones are to be announced within about 3 days. Until then, just leave it at 44 in August. Bubba73 (talk), 05:53, 15 September 2008 (UTC)
Dear prime busters, I have updated the list of the Mersenne primes, up to M45,46. It should be OK, including the 9+9 digits, authors of the discovery, the number of decimal digits etc. but you are invited to recheck because I have used some tricks to get the digits. Please confirm it here that you got the same result. I didn't round the first 9 digits of M45 up - otherwise it would be 06 instead of 05 or something like that. The temporary footnotes for M45,46 were erased. Best wishes, Lubos Motl -- Lumidek ( talk) 13:16, 16 September 2008 (UTC)
I don't see how the fact that a Mersenne prime is a base-2 repunit prime is a generalization. It is the same thing, right? (unless you speak of repunit primes in different bases.)
Bubba73
(talk),
16:50, 16 September 2008 (UTC)
Well, I guess it is OK. It wasn't clear to me the first time I read it. Bubba73 (talk), 17:03, 16 September 2008 (UTC)
It is absolutely silly to try to write out a number name of a number with millions of digits as "X hundred Xty X gazillion, X hundred Xty X bajillion, X hundred Xty X zillion, X hundred Xty X jillion..." It can easily be impractical, and you can easily be forced to lose track. The best way to name huge numbers is just to pronounce each individual digit. Georgia guy ( talk) 17:12, 16 September 2008 (UTC)
I disagree. When I see a large pile of digits one thing that comes to my mind is how would you say it. I have a poster of the first million digit mersenne in my office. A common remark I often hear is how would you even say that number. There is interest in the name of the number. It is an interesting fact that should be preserved (as it was with the 44th mersenne). It should be put back. —Preceding unsigned comment added by 32.155.100.156 ( talk) 18:27, 16 September 2008 (UTC)
I agree with the edit to put the sentence back. I will add to the remark above that the naming system in question if far from silly. The name system referenced was co-invented by the mathematicians John Horton Conway and Landon Curt Noll. The latter found two Mersenne primes a few decades back. We should keep it as an interesting visilation fact: or change it to how high the stack of paper would be if it were printed on standard office laser printer paper. —Preceding unsigned comment added by 32.157.92.185 ( talk) 19:50, 16 September 2008 (UTC)
Someone told me there was a bit of controversy over my edit. I didn't intend to put someone in a huff, however. Being the person who added the original text, I concur with the others who think it belongs.
I like the above comment about a paper stack. Since it is being added to a remark about helping visualize the size of the prime, a paper stack height might do the trick. 4321583 lines at 50 lines per page, double sided yields 43218 pages. Using standard 20lb office paper, that would require 86.436 reams (of 500 sheets). A 20lb ream is about 2 inches thick, so the name of the number would stand 172.872 inches or about 14 feet 5 inches or 4.39 meters high. That might be a better visualization than a page count. —Preceding unsigned comment added by Landon Curt Noll ( talk • contribs) 21:21, 16 September 2008 (UTC)
Peter jackson ( talk) 10:52, 19 September 2008 (UTC)
Just to let you know m31 has been syated wrongly in the list of primes. It reads 2147483647 and should be 2147483646 —Preceding unsigned comment added by 80.4.85.154 ( talk) 15:43, 28 October 2008 (UTC)
I must be missing something here but 231 = 2147483647 and 231 -1 = 2147483646. Or is that not correct? —Preceding unsigned comment added by 80.4.85.154 ( talk) 18:10, 28 October 2008 (UTC)
Ah my mistake -sorry! My calculator has a rounding error on it! I've just tried it on Excel and of course the answer is correct. I should have realised as the answer I got was an even number. Thanks once again! —Preceding unsigned comment added by 80.4.85.154 ( talk) 18:18, 28 October 2008 (UTC)
The article states that the largest prime number known has "almost always been a Mersenne prime" and the foot note states that it has been this way since 1952, except for a small time range. How is since 1952 "almost always"? Asmeurer ( talk ♬ contribs) 06:12, 20 November 2008 (UTC)
The article states that 21039 − 1 is the largest Mersenne number factorized. This does not make sense, as 243,112,609 − 1 (with factorization 243,112,609 − 1 = 243,112,609 − 1) is much, much larger. — Emil J. 14:44, 12 December 2008 (UTC)
I think 2n-1 can always give you a prime IF n = a MERSENNE PRIME I looked at the chart and this seems to work
22-1=3
23-1=7
27-1=127
2127-1=x
and etc... so if you took the answer to 2127-1 and plug that in as the exponent (which means 2x-1), it should give another mersenne prime. I can't do it but those of you with programs designed for it can probably do so. Hope this helps ^_^ 65.37.24.82 ( talk) 06:31, 31 December 2008 (UTC)
I decided not to act immediately due to my incompetence, and let the more knowledgable resolve my concerns.
1 - There are no links to Mersenne in this article. I presume he's a person with his own article? 2 - I got to Mersenne Prime via clicking a link to a Mersenne Number. Does Mersenne number derserve its own article? 3 - Shouldn't there be some mention somewhere of the fact that a mersenne number in binary is of the form 11111<...>111? Manning 06:25, 4 January 2007 (UTC)
Would someone good at number theory like to rewrite my proof of 3) to get rid of all my group theory crutches and make it more leisurely and explanatory? Thanks, Rich 05:35, 21 February 2007 (UTC)
http://primes.utm.edu/glossary/page.php?sort=MersennesConjecture
n the preface to his Cogitata Physica-Mathematica (1644), the French monk Marin Mersenne stated that the numbers 2n-1 were prime for
n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257
Yet the list is as follows:
# | p | Mp | Digits in Mp | Date of discovery | Discoverer |
---|---|---|---|---|---|
8 | 31 | 2147483647 | 10 | 1772 | Euler |
12 | 127 | 170141183…884105727 | 39 | 1876 | Lucas |
Should not Mersenne be credited for those two? Alex 68.46.132.117 ( talk) 05:25, 3 February 2010 (UTC)
No, he merely conjectured that 2p-1 was prime for those values, getting two of his four unproved guesses (for p = 67 and 257) incorrect and missing three more (p = 61, 89 and 109). Euler and Lucas actually proved that the above two (p = 31 and 127) were prime. The first seven on his list had already been discovered so don't really count. -- Glenn L ( talk) 07:01, 3 February 2010 (UTC)
Anonymous user 74.3.4.112 noted the following Google Group message:
However, when I tested M86243 on Prime95, I got: "M86243 is Prime! Wd1: 82145A39,00000000"
Although 1,627,710,365,249 = 86,243 * 18,873,536 + 1 and therefore could qualify as a factor, I am very suspicious.
-- Glenn L 11:56, 16 May 2010 (UTC)
The number of digits of a mersenne prime is approximately equal to its log base 10, since the number of digits of any number, prime or not, is the one more than the integral part of its log base 10. For example, log(base 10) of 10 is 1, while log(base 10) of 100 is 2.
That the number of digits in a mersenne prime is approximately 30% of its exponent follows from the fact that 2**10 = 1024 ≈ 1000 = 10**3. 10% of the exponent gives the number of 1000's, and three times that gives the number of digits. :-) ( Martin | talk • contribs 05:10, 27 April 2010 (UTC))
Please comment on the following valid and important point which has been deleted from the text:
The international inch is defined to be equal to exactly 2.54 centimeters, or equivalently 1 in = 127/50 cm. Thus the Mersenne prime M7=127 enters conversion between the United States customary units and the International System of Units (SI, often referred to as "metric").
Arcshinus ( talk) 02:32, 7 October 2010 (UTC)
The British-American system of units is still widely used because of historical traditions and industrial machining tools. The system's units such as hand, foot, yard, and fathom are derived by multiplying inch by prime factors 2 and 3 while pace, rod, furlong, and mile introduce prime factors 5 and 11. On the other hand the units in the decimal International System are derived by multiplying by powers of 10 (prime factors 2 and 5). It is remarkable that the conversion between the two system was "rounded" in such a way that a new prime factor 127 appeared. The round-off error distribution statistics is greatly affected by what factors are used in conversion between the systems. So the issue here is more subtle than just being some number. —Preceding unsigned comment added by Arcshinus ( talk • contribs) 02:50, 9 October 2010 (UTC)
In the image of the graph showing the digits in the largest known Mersenne prime, why is this graph a line? Shouldn't it be only points at the corresponding points in time when a Mersenne prime was discovered? This way it looks as if new Mersenne primes are continously being discovered, which obviously isn't the case. Toshio Yamaguchi ( talk) 14:17, 4 December 2010 (UTC)
The section "Generalization" seems like it wants to mention the article on repunit primes, but it doesn't do it. It seems like this deserves a note in another section (perhaps "About Mersenne primes"?), but doesn't warrant its own section. Andypar ( talk) 05:05, 27 January 2011 (UTC)
Mersenne 48 and 49 at OEIS. I have done (in Mathematica) LLT and this:
Select[Range[10^3], PrimeQ[2^# - 1] &]
Martin Sojournerfix ( talk) 19:25, 10 March 2011 (UTC)
? Mod(2,349958939111)^43581437-1 %1 = Mod(0, 349958939111) ? Mod(2,100313477119)^49318327-1 %2 = Mod(0, 100313477119)
? Mod(2,5789358091081)^43581437-1 %3 = Mod(0, 5789358091081)
Article states: It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes.
If p is a SG prime and ≡ 3 (mod 4), 2p + 1 will indeed divide 2^p - 1, but if p ≡ 1 this is not true! 89 is SG and 2^89 - 1 is prime. Hence, the claim in the paragraph cited is in error; you need the stronger fact that there are infinitely many SG primes ≡ 3 (mod 4). —Preceding unsigned comment added by 213.67.74.59 ( talk) 23:51, 16 April 2011 (UTC)
I am unsure if this section is appropriate per MOS:MATH#Proofs and I added a cleanup template. The section gives no information about the importance or any other contextual information. I welcome comments from other editors. Toshio Yamaguchi ( talk) 17:11, 5 May 2011 (UTC)
I added the citation for Euclid's theorem about Mersenne primes and perfect numbers. He phrases it thus: "If as many numbers as we please beginning from an unit be set out continuously in double proportion, until the sum of all becomes prime, and if the sum multiplied into the last make some number, the product will be perfect." The opening "if" is equivalent to "if we add 1+2+4+8+... to any number of terms", which is another way of saying (...1111) in binary. No idea how to track down Euler's contribution. Grommel ( talk) 03:24, 5 June 2011 (UTC)
I was surprised that my change of "Ancient Greek mathematicians" to "Pythagoras and/or other ancient Greek mathematicians" respective to "Euclid and/or other ancient Greek mathematicians" was reversed and even called "vandalism". The first ancient Greek mathematicians refered to in this case is Pythagoras who was the first known author speaking about "prime numbers" and mentioning 3 and 7 as prime numbers. The second "ancient Greek mathematician" is Euclid who in his book Elementa is the first to mention perfect numbers, which is also mentioned in the wikipedia article on Euclid. Euclid also mention 31 and 127 in the context of perfect numbers. Of course you can argue that it is uncertain what was written by Pythagoras and Euclid. Writings which have their name could have been written by others. It is even uncertain if there ever existed any living persons like "Pythagoras" and "Euclid", or at least someone can question it. If you go to your book shelf though and look up the specific writing where 3 and 7 are mentioned as prime numbers for the first time, this book has the name "Pythagoras" on the cover and if you go for the book where perfect numbers are mentioned for the first time this book is called "Elementa" and has the name "Euclid" on the cover. So I think it is a legitimate opinion to think that their names should be added to the article on Mersenne primes and I disagree with calling it "vandalism". — Preceding unsigned comment added by 193.11.50.158 ( talk) 15:05, 19 September 2012 (UTC)
When quoting sources a source closer to the actual historical happening is considered better. Nowadays it is often possible to see the traces, relicts, from an occasion on the internet since it is still there.
GIMPS (Global Internet Mersenne Prime Search) is a distributed search for Mersenne primes using softwares like prime95. The computer programs are running on the participants computers and whenever there is a result/output it is sent to a server (primenet-server), where the result is included in the log-file and database. In the GIMPS pressrelease concering Mersenne primes number 45 and 47 it is not mentioned which dates they were found. Fortunately on the user forum, mersenneforum.org, the logfiles (with the faked LL-residues) are quoted: logfile M#45 found on "06-Sep-08 19:53" UTC and logfile M#47 found on "23-Aug-08 7:33" UTC.
All other sources to when these Mersenne primes were found are directely of indirectely based on the information in the logfiles, hence a primary source or relict. 83.216.98.37 ( talk) 17:35, 9 October 2012 (UTC)
Quite some time ago the date for the find of Mersenne prime #30 was changed from "September 20 1983" to "1983 September 19" and for #31 from "September 6 1985" to "1985 September 1" without giving any reliable sources for these changes. So far I have not been able to find any conclusive arguments for which of the dates are correct. The oldest and, as it appears, most reliable sources have "September 20 1983" and "September 6 1985" respectively, but I don't like to make any changes until I feel I can prove which is right especially since I don't know on which ground the changes were made.
Well, this is just to let you know that I am working on this. Any help is appreciated. 193.11.50.158 ( talk) 10:01, 21 September 2012 (UTC)
Speusippus, c. 408 – 339/8 BCE, wrote a book named On Pythagorean Numbers. This book was mainly based on the work of
Philolaus, c. 470–c. 385 BCE, according to
Iamblichus, c. 245–c. 325 CE, who obviously had access to both the book of Speusippus and the work of Philolaus and could compare their works. Iamblichus gives us a long, direct quotation of Speusippus and in this quotation we find the oldest known reference to the concepts of prime numbers and composite numbers. It is clear of course that since Philolaus knew about (or "discovered") prime numbers he also knew about the smallest ones like 2, 3, 5, 7, 11.
So why do I also like to include the following passage of the quotation from Speusippus: "Ten does have an equal amount /.../ it is the first in which an equal amount of incomposite [i.e. 1,2,3,5,7] and composite [i.e. 4,6,8,9,10] numbers are seen. /.../ seven is a multiple of none"?
If we take the easiest part first: "seven is a multiple of none", that is a different way of saying that "7 is a prime number". It would be nice to include it since it is the first time ever in the history of numbers that 7 is said to be a prime number. Yes, I only like to quote that small part since its a part of a larger discussion which would only obscure things if we quote.
OK, number 3 then? Is there any reference to number 3 as a prime number. Well, once again if you know that there are prime numbers surely you know that 3 is a prime number. Beside that, in the passage I like to quote, we find a discussion about why 10 is to be recognized as a "perfect number" and here we are not talking about "perfect number" in a modern sense, but the old Greek mathematicians were thinking about numbers with good quality, ideal numbers. So, Iamblichus and my interpretation of Philolaus (according to Speusippus) is that, one of the arguments why 10 should be called a "perfect number" is that among the 10 numbers less than and equal to 10 (1, 2, 3, 4, 5, 6, 7, 8, 9 and 10) we find an equal amount of prime numbers and composite numbers "it is the first in which an equal amount of incomposite and composite numbers are seen." The prime numbers (incomposite) referred to here must be 1, 2, 3, 5 and 7. The composite numbers must be 4, 6, 8, 9 and 10. So, the conclusion from this passage is, even if it is an implicit reference, that Philolaus knew that 3 and 7 are prime numbers.
So the reason why I also want to include these two parts of the quotation:
A. "Ten does have an equal amount /.../ it is the first in which an equal amount of incomposite [i.e. 1,2,3,5,7] and composite [i.e. 4,6,8,9,10] numbers are seen."
B. "seven is a multiple of none"
is that they give a direct reference to the numbers 3 and 7 as prime numbers and its the first time ever they are said to be prime numbers.
83.216.101.203 (
talk)
09:57, 25 November 2012 (UTC)
The few edits that as of now trickled are only a tiny start. Expect a large flood. I suggest to lock article until Tue, Feb 5th (which is known to be the date of the official press release), to save your reverting efforts.
Additional page to consider locking is the "Largest_known_prime_number". — Preceding unsigned comment added by 99.121.250.148 ( talk) 20:10, 1 February 2013 (UTC)
Regarding M48 which has recently been added, it is being discussed here. Here it is claimed primality has been verified. -- Toshio Yamaguchi 11:09, 27 January 2013 (UTC)
It has not yet been added to the milestones list though. -- Toshio Yamaguchi 11:23, 27 January 2013 (UTC)
The definition of the article's subject does not appear until the second paragraph of the lead. Wouldn't it be less confusing to start with "A Mersenne prime is a prime number of the form 2^n - 1" and go from there, pointing out that (a) n is necessarily prime and (b) (by back formation?) a number of the form 2^n - 1 is called a Mersenne number? -- Vaughan Pratt ( talk) 17:59, 4 February 2013 (UTC)
The Infobox integer sequence at the top of the article is confusing: it looks like Ulrich Regius published on Mersenne primes before Mersenne was born. While this is true, there should be something in the History section to clarify. I'm not knowledgeable enough, but this should be easy for someone who is. By the way, is there an English translation of Regius' work? A Wikipedia article on Regius? I couldn't find either. Myron ( talk) 13:56, 6 February 2013 (UTC)
This may be a dangerous question to pose, but it would be nice to know (ie. add to article) what practical use is or can be made of Mersenne numbers, if any. I get that the search is 'fun' (fsvo) in itself but are there specific use cases for this series of numbers? -- AlisonW ( talk) 22:48, 7 February 2013 (UTC)
I noted there is some inconsistency in the representation of the numbers in this article. For example long numbers in Mersenne prime#History and Mersenne prime#Factorization of composite Mersenne numbers use comma separated digit groups, while the numbers in Mersenne prime#List of known Mersenne primes don't use commas. Wikipedia:Manual of Style/Dates and numbers#Delimiting (grouping of digits) says numbers with five or more digits should be separated into groups using commas and also says that in scientific articles thin spaces can be used instead. Which style should be used in this article? I suggest to apply that style to all numbers in this article, after an appropriate one has been identified. -- Toshio Yamaguchi 15:14, 9 February 2013 (UTC)
The text there matches from this reference: 1. It may or may not be appropriate here but would need a citation at the least. (I researched it because of the edit mark at the start of the section made May 2011].-- Billymac00 ( talk) 00:53, 11 February 2013 (UTC)
It can be easily seen that if p is an odd prime, then 2p - 1 ≡ 7 or 31 (mod 40). It can be easily proven that 2p - 1 ≡ 7 or 11 (mod 20). This is because 2p - 1 ≡ 3 (mod 4) and 2p - 1 ≡ 7 or 1 (mod 10). So, in the case that 2p - 1 ≡ 7 (mod 10), 2p - 1 ≡ 7 (mod 20) since for all integers k, 20k + 7 ≡ 3 (mod 4) and 20k + 17 ≡ 1 (mod 4) ≠ 3 (mod 4). In the case that 2p - 1 ≡ 1 (mod 10), 2p - 1 ≡ 11 (mod 20) since for all integers k, 20k + 11 ≡ 3 (mod 4) and 20k + 1 ≡ 1 (mod 4) ≠ 3 (mod 4). However, I need someone to go further and prove that 2p - 1 ≠ 11 or 27 (mod 40). This is a necessary condition to prove that 2p - 1 ≡ 7 or 31 (mod 40). PhiEaglesfan712 15:52, 13 July 2007 (UTC)
The 3rd reference is a dead link. Blackbombchu ( talk) 03:29, 4 December 2013 (UTC)
Sometimes Wikipedia has 2 different ways to write an article an despite that neither of them is enforced throughout the entire Wikipedia system, each individual article is supposed to pick only one of the 2 styles to stick to and not mix them, for example Wikipedia's policy doesn't allow a ship to be refered to as it in one part of an article and she in another part of the same article. For consistencey, since most of the mathematical expressions that are not not their own sepearte line are using html code, I think the rest of the mathematical expressions in the article that are not on their own separate line should also be switched from latex to html code. Furthermore, I know the html code for those expressions really well so I should be the one to make that change. Is it fine for me to make that change, only for the ones that are not by themselves on a line? Blackbombchu ( talk) 20:40, 7 December 2013 (UTC)
2P-1 is an odd number ⇒ 2P-1 ≡ 1(mod 2)
By Fermat's little theorem, we see that, 2P ≡ 2(mod p) ⇒ 2P-1 ≡ 1(mod p)
if p is an odd prime then: 2 ≡ -1(mod 3) ⇒ 2P ≡ (-1)P(mod 3) ⇒ 2P-1 ≡ -2(mod 3) ⇒ 2P-1 ≡ 1(mod 3)
So we got:
2P-1 ≡ 1(mod 2)
2P-1 ≡ 1(mod 3) ... ( for p>2 )
2P-1 ≡ 1(mod p)
So, for p>3 , we can found that 2P-1 ≡ 1(mod 6p)
Note: 2P-1 doesnt have to be a prime number!
Isaac.mor (
talk)
08:30, 24 October 2014 (UTC)
Mn = 2n-1
its well known that you can build Mn digits using only the digits of n
lets show a few examples:
if the last 2 digits of n are ....17 then Mn last 3 digits have to be ....071
if the last 2 digits of n are ....23 then Mn last 3 digits have to be ....607
i will only show the roles for an odd n because we wanna use it for primes
| or |
|
just so you know the same works for 3 digits of n lets show a few examples:
2... 639-1 = 2... 139-1 = ... 1887
2... 711-1 = 2... 211-1 = ... 8047
etc ...
the same works for any k digits of n
but for really big numbers you need a LOT of computer power :)
Isaac.mor (
talk)
12:03, 24 October 2014 (UTC)
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A new Mersenne prime was discovered on Jan. 07 2016. See http://www.mersenne.org/primes/. This calls for a substantial edit to this page as well as many other wikipedia pages, because "largest prime", "second largest prime", and "largest mersenne prime" are used extensively referring to now-incorrect numbers.
66.31.237.80 ( talk) 05:34, 24 January 2016 (UTC)
I think the graph in the article is wrong. There is a slow increasing line between 1950 -1960 indicating every year a bigger Mersenne prime was found with an increase in size equal to the previous each year, then between approx. 1960 -1962 for two years the rate increased. in my opionion there should be horizontal lines between discoveries of the finds and no steady increase. for the last few years it does not matter that much as the rate of finds are increased so much that the graph will be about the same (i think the point of the graph) 195.240.149.123 ( talk) 04:30, 13 August 2010 (UTC)
I freely admit to not being a mathemetician, or indeed particularly number-savvy with regard to primes, but there is an inconsistency in the article with regard to the number 2. Within the confines of this article, is "2" considered a Mersenne prime? Part of the article suggests it is, and part not.
In the history section, 2 is listed as a prime (and the section states that "His list was accurate through 31",) and the image includes 2 as a Mersenne prime, yet the rest of the article - especially the lede: "The first four Mersenne primes (sequence A000668 in the OEIS) are 3, 7, 31, and 127." - doesn't include 2.
I see that there is reference to two different OEIS sequences - one of which includes 2, and one that doesn't, however this is confusing to those who don't have an in-depth understanding of the subject matter. In short - as it currently stands the article is inconsistent, and should:
( talk) 06:28, 1 January 2017 (UTC)
Not yet, but now that it's been explained to me, I'll certainly think about. I solidly fall into the "not fluent" category, and it puzzled the hell out of me. Chaheel Riens ( talk) 18:29, 1 January 2017 (UTC)
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Does anyone understand what [27] means? It's not a minor edit, it's unsourced, it's been undone by four different editors, and User:PrimeHunter has been unable to find anything about the claim [28]. Meters ( talk) 04:28, 3 December 2017 (UTC)
It is not a claim, it is a fact that is useful for generating pyramid charts. You wont find out by googling it, you will find out by doing it. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 04:42, 3 December 2017 (UTC)
Your right, it is not a good idea for you, but it is a good idea for the page. As a great man once said, "if you cannot see what is right in front of you then you are indeed a fool." Please physically investigate this for yourself before any further complaints. this is a useful addition not a reckless destruction, so please do not treat it as such. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 04:47, 3 December 2017 (UTC)
Please stop the vadalism, or i will have to email wikipedia about this. i am making a valid useful contribution anyone who checks it out for themselves will understand on be on my side. i cannot provide a source for nature and basic geometry so i am sorry, but your just going to have to use your eyes and brains. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 04:58, 3 December 2017 (UTC)
If i get blocked than that just proves that wikipedia is a useless pile of rubbish and that indeed the vast majority of people are in fact not intelligent at all, but petty belligerent fools. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:07, 3 December 2017 (UTC)
wikipedia, a pun for world wide web encyclopedia. encyclopedia, a book giving information. My addition is information that is immediately verifiable and self evident, and is therefore viable information. how is Wikipedia ever to improve if it seeks to remove and destroy basic facts? then it would be called wikibook. so i am sorry but you are all wrong. please read my addition more carefully, try it for yourself and ponder it for at least a day before even thinking about removing it as the is no logical or reasonable basis for doing so. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:23, 3 December 2017 (UTC)
PLEASE STOP UNDOING! there is no need to. it does not change anything, it only adds an additional valid & verifiable point, which is in the spirit of wikipedia. It is a description of an image therefore it require no citation. please read and understand the rules before attempting to enforce them. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:28, 3 December 2017 (UTC)
PLEASE STOP UNDOING! there is no need to. it does not change anything, it only adds an additional valid & verifiable point, which is in the spirit of wikipedia. It is a description of an image therefore it require no citation. please read and understand the rules before attempting to enforce them. Draw a pyramid chart, count the spacing, if you still do not understand than i don't think you have any authority to undo it, because you obviously don't understand it therefore have no right to comment.— Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:30, 3 December 2017 (UTC)
@
Kulprit001:, the belligerent and pig-headed way you approached this discussion was always doomed to failure: Wikipedia works on a collaborative model, and if you can't explain to others what you're doing politely then it will never work. That being said, @Everyone else: Kulprit is almost certainly trying to express that the number of nodes in a full (or complete) binary tree with n layers is the Mersenne number 2^n - 1. (Or something equivalent.) This is a totally true thing. And in fact Mersenne numbers are a common answer to lots of enumerative combinatorial questions, although they aren't usually called "Mersenne numbers" in that context. It is a reasonable question about whether these combinatorial facts should be listed somewhere, either in the section Kulprit was trying to add to, or in a separate subsection called "in enumeration" or something. --
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I removed the following text from the introduction:
and this from "Mersenne numbers in nature":
Both are based on the belief that a Mersenne number is 2n−1, which is a mistake. The correct "pernicious" part is that there be a prime number of 1's followed by a large number of 0's that seems too trivial to bother mentioning (especially in an introduction). Zaslav ( talk) 04:13, 6 October 2018 (UTC)
The section about "primitive part" is impossible to understand to the largest part of it. For example,
The phrase is grammatically incorrect and incomplete, and it is not clear what the author wanted to say. It's similar for the whole subsection and a later one, probably from the same "contributor". Is anyone please willing to improve this? Such "contributions" are annoying, the article would be better without it. I'd suggest to move the subsection here (i.e., delete it from the main page) until it is rewritten in correct English. As it stands, it barely qualifies for a comment on this talk page. But I don't know whether doing so is (WP-)"politically correct". — MFH: Talk 17:48, 5 December 2018 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
I'm no mathematician, but shouldn't the definition of Mersenne prime include that it has to be one less than an natural power of two? Also, in the chart of Mersenne primes, shouln't the first entry be 2^0 - 1, which is 0?
No. 0 is not a prime number. It's divisible by every other integer-- 129.15.228.164 22:48, 3 September 2006 (UTC)
It is easy to see that 2p-1 is prime iff p is prime... I'm not sure its really easy at all... maybe I'll wait for the proof to come up on the Prime numberss page; but in the mean time, the sentence should be reworded for a regular guy (like me) to know whats going on. --cM
It is not hard. If p is not prime, then you can write p as qr. It is easy to see that 2^q-1 and 2^r-1 are then divisors of 2^p-1 and therefore 2^p-1 is not prime either. The reason is obvious if you write 2^p-1 in the binary form. It looks like the digit "1" repeated p times (1111...). Similarly, 2^q-1 is the number 1 repeated q times. For example, 2^15-1 is 111111111111111, and 2^3-1 is 111, and the latter is obviously a divisor of the former because the ratio is 1001001001001. See also my text at the bottom. -- Lumidek 14:04, 6 Jun 2004 (UTC)
Ok, I'll reword it. In fact, "iff" is wrong. If 2p-1 is prime, then p must itself be prime.
--Axel
"Iff" being the abbreviation used in logic for "if and only if"?
Yes.
Generally, it seems to me bad form to ever use the words "clearly", "it is easy to see", and similar in math articles here. These are assuming a certain audience. Even if something is really, really clear, it's probably best not to use this. There will be someone learning it for the first time (we all learned "clear" things a first time) and "clearly" or "easy" may be off-putting. Revolver 04:57, 8 Jun 2004 (UTC)
2^31 - 1 = 2,147,483,647 !? Isnt that a prime? (see Two_billion_one_hundred_forty-seven_million_four_hundred_eighty-three_thousand_six_hundred_forty-seven, alas it will probably be deleted soon :b!) // Noone
What exactly is a "Mersenne number"? I've seen three different difinitions as of late. Obviously to be a candidate for a Mersenne prime a number must be "one less than a prime power of two", but isn't a "Mersenne number" simply "one less than a power of two"? -- Pascal666 05:02, 6 Jun 2004 (UTC)
After some exhaustive googling, I managed to fix all the links to point to articles using each mathematician's full name. However, I was completely unable to find "R.E. Powers"'s full name. Does anyone happen to know it?
The text says 'before 1461'. The table says 1456. Which is it?
If M(n)=2^n-1, is there a sequence n,M(n),M(M(n)),...,M(M(...M(n)...)) (k is the length of the sequence) where all the numbers are prime? What are the values of n for different values of k? Is there such a sequence for all k?
One source I read had Codice Palatino as the discoverer of M13 in 573. Another source had Cataldi as the first to prove the primality in 1588. The table has 1456 as the date of discovery of M13... but the table has no discoverer. This is why I believe that the table is the least credible of the 3... The other two have not only a date of discovery, but also a discoverer.
I have reverted a suspicious edit [3] by 202.163.246.145 claiming that M32 was found on April 1 instead of February 19 and M33 on February 1 instead of January 10. The contributor did not offer any justification for the change and all sources I checked (e.g. [4]) confirm the original dates. So I believe the edit has been just a vandalism/test. -- Mormegil 10:57, 16 July 2005 (UTC)
On December 16th, the 43rd known Mersenne prime was announced. If you can't live without a guess, it could be, among other choices, M 30402457, found by Curtis Cooper, but because you have no reason to believe my random generator, there is no reason for you to propagate the hypothesis. ;-) -- Lumidek 04:38, 21 December 2005 (UTC)
According to the
Gimps Status page, all exponents up to 15,300,000 have been
Lucas-Lehmer tested at least once. This definitely confirms that M13,466,917 is the 39th Mersenne prime.
—
Herbee
20:55, 4 January 2006 (UTC)
Qutezuce, do you know the unit for the countdown: days ? exponents ? --FvdP 21:13, 5 January 2006 (UTC) (I guess exponents --FvdP 21:24, 5 January 2006 (UTC))
Your guess would be correct. To quote the site http://www.mersenne.org/status.htm:
July 10, 2006: Double-checking proves M(13466917) is the 39th Mersenne prime.
April 23, 2007: All exponents below 15,000,000 double-checked.
From the foregoing it appears that exponents are being double-checked at the rate of about a million every six months.
So M(20996011) may not be confirmed as the 40th until Spring 2010 unless exponents are double-checked more quickly.
Glenn L 09:23, 2 July 2007 (UTC)
There is an IP address that is making some changes to the credit for M32. I believe this table is based on the database at primes.utm.edu, more specifically this page. That page credits Slowinski and Gage with M32. The IP address claims to be involved in this find, and said that they decided to credit only Harwell because it was his machine. However I believe primes.utm.edu uses a different criteria to give credit. For example the most recent of the Mersenne primes found by GIMPS was found on a computer owned by a university, but they gave credit to the people who administered the program to run the prime-checking software on hundreds of machines across the campus. So for now I've reverted the change, but I hope that the IP address returns and we can discuss this futher on this talk page. Qutezuce 20:31, 30 January 2006 (UTC)
Yes, This is my exact point; Slowinski and Gage had nothing to do with this find apart from supplying the code to me. I installed the code on the Cray-2 in a modified way, allowing to be run only when the system was completely idle. I found the M32 exponant and imediately passed it on to David and Paul for verification. Subsequently Harwell was given credit for the find as it was their machine. Perhaps George Woltman should be given credit for all of the subsequent finds !. 09:20 GMT 3rd Feb 2006
As a follow up to this discussion, http://primes.utm.edu/notes/756839.html has been created, and http://primes.utm.edu/mersenne/index.html has been updated with the credits - et al. 13:47 20th Feb 2006 (GMT)
The correct notation is "Mersenne 32", not M32... In fact, M32 is not even prime because 32 is composite. —Preceding unsigned comment added by PhiEaglesfan712 ( talk • contribs)
Could someone please explain, possibly in the article, just how the naming convention works for these things? I mean, where does the choice of the number in the subscript come from, as in the 13 in M13, for example? Narxysus 07:56, 7 May 2006 (UTC)
The very beginning of the main article defines the convention:
However, M13 should not be confused with M13:
Glenn L 06:36, 9 July 2007 (UTC)
You guys are still using the notation the wrong way...
M13 = 213 - 1 = 8191 is "Mersenne 5" not M5
M5 = 25 - 1 = 31, which in fact is "Mersenne 3"
Mersenne 13 is M521 = 2521 - 1 (≈ 6.8648 × 10156). —The preceding unsigned comment was added by PhiEaglesfan712 ( talk • contribs).
"On September 4, 2006, a computer reported finding the 44th known Mersenne prime. Verification will begin shortly, probably taking a week or so to complete. If it is verified, this will be GIMPS' tenth prime!" http://www.mersenne.org/prime.htm
NevilleDNZ 23:34, 4 September 2006 (UTC)
Could someone please explain (and add to the article) what Mersenne primes are useful for / why they are of any interest. Is it just because of their extraordinary size? Can you do stuff (not just pure arithmetics) with Mersenne primes that you can't do with other primes?
I saw the call for a citation following the statement of how many pages would be required to print M44. So I fired up Microsoft Word 2003, imported the text of M44 (downloaded from www.mersenne.org), set the margins to one inch and the typeface to 12-point Times New Roman, and voila: two thousand and seven hundred and thirty and four pages (to be precise, 2,733 full pages each containing 46 lines of 78 digits, plus a partial page containing 30 full lines and a partial line containing 14 digits). This result differs slightly from the number of pages indicated by Jmalc, which I attribute to slight differences in line spacing between Jmalc's word processor and mine.
Unfortunately, this constitutes original research and thus is not usable here. My chances of getting this fact published in a reputable journal is small (at best), so there will be no citation. Too bad. Jmalc's result is also original research. Perhaps, under the new policies, this whole statement should be purged. — SWWright Talk 20:12, 16 April 2007 (UTC)
Not sure if this section should even be part of the article in the first place but it's not hard to see the current info is wrong since by the most significant digits in the factors (5 and 2), the most significant digit in the product should thus be a 1 instead of a 5. Not sure if the value or the factors are wrong....can someone verify? Sentri 01:42, 23 May 2007 (UTC)
Oh nvm...my bad...didn't see the first factor Sentri 01:43, 23 May 2007 (UTC)
I think codice is the plural of codex. Kope 05:21, 14 June 2007 (UTC)
This isn't true if one of x or y is zero, or if x=y. However, outside of those degenerate cases, I'm not entirely sure that x^a-y^a|x^b-y^b implies a|b (of course, the proof of the converse is straightforward). 192.236.44.130 07:30, 12 August 2007 (UTC)
PhiEaglesfan712 has changed the definition of Mersenne number and posted in an old section. See section 2 #Mersenne number for discussion. PrimeHunter 02:08, 15 August 2007 (UTC)
I have moved the discussion here. Arcfrk 02:17, 20 August 2007 (UTC)
I strongly suggest you discuss on talk pages before changing definitions of article subjects that require significant changes to the article text and other articles, as you did in Mersenne number [7] and Double Mersenne number [8]. And using edit summary "fix definition of Double Mersenne number - with source" [9] followed by deletion of a link to a reliable and popular source that uses the former definition [10] is misleading. In addition, it's unclear whether your source here [11] actually requires prime exponent in Mersenne numbers. The glossary at the same site, http://primes.utm.edu/glossary/page.php?sort=MersenneNumber, does not require prime exponent but just says that many authors do.
Fermat numbers are of form 2^(2^n)+1 and Fermat primes are prime Fermat numbers. 2 = 2^0+1 cannot be written as 2^(2^n)+1, so it's not a Fermat number and therefore not a Fermat prime. I don't see any reason why this should affect the definition of Mersenne numbers. And Wikipedia definitions should be based on reliable sources and not on what "makes sense" to an editor making original research analogies. Reliable sources use two different definitions so we should say both are in use and not delete one of them like you did. For practical reasons we either have to choose one of them in our articles, or write two versions of many things which would be an unnecessary mess. I recommend we choose 2^n-1 for integer n and not restricted to prime n. It's common, for example in http://mathworld.wolfram.com/MersenneNumber.html. It's practical to use the more general definition when writing things that are relevant for both versions. Other articles, for example Repunit#Generalizations, would require changes if we change to PhiEaglesfan712's definition (and Mersenne number would require further changes). Many things depend on a common definition we have used for a long time and we should not change it without very good reason. PrimeHunter 23:46, 14 August 2007 (UTC)
Paulo Ribenboim, The Book of Prime Number Records, 2nd edition, Chapter 2, Section VII Mersenne Numbers, says 'The numbers (with q prime) are called Mersenne numbers'. DRLB 17:19, 20 August 2007 (UTC)
I have rewritten the lead, trying to make it less terse and more readable. I have also restored the old definition of the Mersenne number. One of the most authoritative sources on the subject, Crandall and Pomerance, define the "Mersenne numbers" to be the numbers of the form
They are using a diffirent letter as a mnemonic devise to indicate that we are mostly interested in these numbers for certain special values of q, but the definition is worded for arbitrary natural exponent q. A footnote with an explantion of conventions may be added, but I felt reluctant to put it into the lead. Alternatively, an explanation can be given later in the main text. PrimeHunter gave above a compelling consistency argument for keeping the present convention.
Other changes to the lead: streamlined typography (hopefully, correct and consistent); removed clutter; added a brief mention of Lucas–Lehmer test; moved repunit property closer to the definition of Mersenne numbers, in order not to break the continuity of the exposition of Mersenne primes. Arcfrk 02:26, 20 August 2007 (UTC)
At the bottom of the List of Known Mersenne Primes section, a statistic is given that it would take 2769 pages to display M44 in a standard word processor, and then it's marked as "Citation Needed". Unfortunately, an exact figure (and by extension, the validity of any citation) may be impossible, as this number will vary a little bit, since some word processors and some printers will alter the space between characters or lines ever so slightly (as well as several other less-critical factors).
However, since we know the number of digits in M44, and numbers are usually fixed-width, even in proportionally-spaced fonts, it's easy enough to attempt to duplicate the statistic with a simple macro. Using Microsoft Word XP for the PC, I got 2734 pages using all 0's. This certainly seems to be in line with the original poster's comment, though not exactly the same for the various reasons just noted. -- Rob 22:17, 15 September 2007 (UTC)
This strikes me as a tad pompous:
Perhaps even more embarrassingly, it is not known whether infinitely many Mersenne numbers with prime exponents are composite
Could this be reworded to avoid the implication that Wikipedia is ashamed of mathematicians who can't prove a property so painfully simple, when most of humanity can't even understand what that property is? -- Doradus 02:51, 22 September 2007 (UTC)
This states that xa − ya | xb − yb if and only if a|b —Preceding unsigned comment added by Barneypitt ( talk • contribs) 22:57, 18 January 2008 (UTC)
Thanks all for fascinating article, I would appreciate a x-reference next to the statement...
This states that xa − ya | xb − yb if and only if a|b
under the "Searching for Mersenne primes" section. If anyone would like to let me know how I add a "reference required" comment instead of using the chat page then thanks (sorry, newbie).
Thanks again, B —Preceding unsigned comment added by Barneypitt ( talk • contribs) 23:02, 18 January 2008 (UTC)
Shouldn't the article explain who Mersenne was? A bit lower down, the article says that Euclid worked on them, so how did the Mersenne number/prime come to be named after Mersenne? AnteaterZot ( talk) 12:00, 14 March 2008 (UTC)
I was reading a book in which Mersenne Numbers and prime numbers where referred in a way it made me confuse, so I came to Wikipedia for clarify my doubts, only to find that this article confused me too. It was only after re-reading and checking the discussion page that I finally concluded that not all Mersenne numbers are prime numbers too.
So, I ask: Why not making an exclusive article for Mersenne numbers instead of redirecting it to the article of Mersenne primes?
-- Francisco Albani ( talk) 00:54, 24 March 2008 (UTC)
I have removed a new section called "Distribution of Mersenne primes" with this text:
p is the exponent in a Mersenne prime. The conjecture appears non-notable and I see no good reason to believe it. The conjecture was clearly made to fit 4 known data points: There is 1 Mersenne prime exponent p with 2^1 < p < 2^2, there are 3 with 2^2 < p < 2^4, there are 7 with 2^4 < p < 2^8, and there are 15 with 2^8 < p < 2^16. The conjecture then predicts 31 with 2^16 < p < 2^32. This may take decades to test. I guess the conjecture was made after experimenting with a lot of guesses involving different sets of data points. Given the law of small numbers, there is likely to be a small data set which matches some pattern by "coincidence", without following the pattern forever. If a good independent source is found then the conjecture might be mentioned in Mersenne conjectures. PrimeHunter ( talk) 13:19, 27 April 2008 (UTC)
play in the article. Although MathWorld and Wikipedia define them as all numbers of form (2^n - 1), Sloanes Handbook of integer sequences leans towards requiring n to be prime. A couple sentences about what number theory texts prefer would be good. Rich ( talk) 09:43, 13 May 2008 (UTC)
The article currently says "Mersenne gave no indication how he came up with his list..." This contradicts Dickson, History of the Theory of Numbers, I, 13 and note 61, who lists the criteria by which Mersenne selected his numbers. In 1647 Mersenne stated without proof that Mp is prime when p is a prime of one of the three forms 4m + 1, 4m + 3, or 2m - 1 (the last, namely itself a Mersenne prime, being somewhat obscurely expressed by Mersenne). Applying this test to all Mersenne numbers below M8191 yields exactly Mersenne's four picks, namely M31, M67, M127, and M257.
So in the range Mersenne considered, his first two rules, yielding M67 and M257, scored 0% while his recursive rule, that Mp is a Mersenne prime when p is, yielding M31 and M127, scored 100%. Though the first two rules served him poorly, thanks to the third rule he ended up with a better overall score than he could have expected had he simply picked four primes at random between 19 and 257.
So while it's true that Mersenne gave no indication how he came up with his rules, that's not to say that he gave no indication how he came up with his list. If there are no objections by the end of the month I suggest adjusting the article accordingly. -- Vaughan Pratt ( talk) 04:16, 14 May 2008 (UTC)
Someone needs to make the above change in the text. Additionally, if Mersenne published M31 and M127 in 1647, why does the table attribute their discoveries to others a century or two later (M31 by Euler in 1772 and M127 by Lucas in 1876). Is Mersenne not given credit because his was only a conjecture and not a proof? If so, that should be explicitely stated somewhere. 68.73.93.0 ( talk) 07:32, 27 September 2008 (UTC)
Yes he's not given credit because he didn't prove it. Nico92400 ( talk) 08:03, 29 September 2008 (UTC)
I understand that a "Mersenne number is a number that is one less than a power of two". However, why do these numbers warrant a special name? what is their significance? -- Sreifa01 ( talk) 12:28, 26 May 2008 (UTC)
(copied from talk:Prime_number) There's little more besides a headline stating more information to come soon, but http://mersenne.org/prime.htm claims to possibly have found the 45th mersenne prime number. Slashdot has also covered it. -- 76.85.144.126 ( talk) 00:32, 28 August 2008 (UTC)
On Saturday, GIMPS found one more, 46th Mersenne prime. ;-) [18] The exponent is probably around 40 million, too. It will take two weeks or so to check it. -- Lumidek ( talk) 07:08, 8 September 2008 (UTC)
Peoples, peoples, peoples - stop fighting over 44 in August versus 46 in September. The two new ones are to be announced within about 3 days. Until then, just leave it at 44 in August. Bubba73 (talk), 05:53, 15 September 2008 (UTC)
Dear prime busters, I have updated the list of the Mersenne primes, up to M45,46. It should be OK, including the 9+9 digits, authors of the discovery, the number of decimal digits etc. but you are invited to recheck because I have used some tricks to get the digits. Please confirm it here that you got the same result. I didn't round the first 9 digits of M45 up - otherwise it would be 06 instead of 05 or something like that. The temporary footnotes for M45,46 were erased. Best wishes, Lubos Motl -- Lumidek ( talk) 13:16, 16 September 2008 (UTC)
I don't see how the fact that a Mersenne prime is a base-2 repunit prime is a generalization. It is the same thing, right? (unless you speak of repunit primes in different bases.)
Bubba73
(talk),
16:50, 16 September 2008 (UTC)
Well, I guess it is OK. It wasn't clear to me the first time I read it. Bubba73 (talk), 17:03, 16 September 2008 (UTC)
It is absolutely silly to try to write out a number name of a number with millions of digits as "X hundred Xty X gazillion, X hundred Xty X bajillion, X hundred Xty X zillion, X hundred Xty X jillion..." It can easily be impractical, and you can easily be forced to lose track. The best way to name huge numbers is just to pronounce each individual digit. Georgia guy ( talk) 17:12, 16 September 2008 (UTC)
I disagree. When I see a large pile of digits one thing that comes to my mind is how would you say it. I have a poster of the first million digit mersenne in my office. A common remark I often hear is how would you even say that number. There is interest in the name of the number. It is an interesting fact that should be preserved (as it was with the 44th mersenne). It should be put back. —Preceding unsigned comment added by 32.155.100.156 ( talk) 18:27, 16 September 2008 (UTC)
I agree with the edit to put the sentence back. I will add to the remark above that the naming system in question if far from silly. The name system referenced was co-invented by the mathematicians John Horton Conway and Landon Curt Noll. The latter found two Mersenne primes a few decades back. We should keep it as an interesting visilation fact: or change it to how high the stack of paper would be if it were printed on standard office laser printer paper. —Preceding unsigned comment added by 32.157.92.185 ( talk) 19:50, 16 September 2008 (UTC)
Someone told me there was a bit of controversy over my edit. I didn't intend to put someone in a huff, however. Being the person who added the original text, I concur with the others who think it belongs.
I like the above comment about a paper stack. Since it is being added to a remark about helping visualize the size of the prime, a paper stack height might do the trick. 4321583 lines at 50 lines per page, double sided yields 43218 pages. Using standard 20lb office paper, that would require 86.436 reams (of 500 sheets). A 20lb ream is about 2 inches thick, so the name of the number would stand 172.872 inches or about 14 feet 5 inches or 4.39 meters high. That might be a better visualization than a page count. —Preceding unsigned comment added by Landon Curt Noll ( talk • contribs) 21:21, 16 September 2008 (UTC)
Peter jackson ( talk) 10:52, 19 September 2008 (UTC)
Just to let you know m31 has been syated wrongly in the list of primes. It reads 2147483647 and should be 2147483646 —Preceding unsigned comment added by 80.4.85.154 ( talk) 15:43, 28 October 2008 (UTC)
I must be missing something here but 231 = 2147483647 and 231 -1 = 2147483646. Or is that not correct? —Preceding unsigned comment added by 80.4.85.154 ( talk) 18:10, 28 October 2008 (UTC)
Ah my mistake -sorry! My calculator has a rounding error on it! I've just tried it on Excel and of course the answer is correct. I should have realised as the answer I got was an even number. Thanks once again! —Preceding unsigned comment added by 80.4.85.154 ( talk) 18:18, 28 October 2008 (UTC)
The article states that the largest prime number known has "almost always been a Mersenne prime" and the foot note states that it has been this way since 1952, except for a small time range. How is since 1952 "almost always"? Asmeurer ( talk ♬ contribs) 06:12, 20 November 2008 (UTC)
The article states that 21039 − 1 is the largest Mersenne number factorized. This does not make sense, as 243,112,609 − 1 (with factorization 243,112,609 − 1 = 243,112,609 − 1) is much, much larger. — Emil J. 14:44, 12 December 2008 (UTC)
I think 2n-1 can always give you a prime IF n = a MERSENNE PRIME I looked at the chart and this seems to work
22-1=3
23-1=7
27-1=127
2127-1=x
and etc... so if you took the answer to 2127-1 and plug that in as the exponent (which means 2x-1), it should give another mersenne prime. I can't do it but those of you with programs designed for it can probably do so. Hope this helps ^_^ 65.37.24.82 ( talk) 06:31, 31 December 2008 (UTC)
I decided not to act immediately due to my incompetence, and let the more knowledgable resolve my concerns.
1 - There are no links to Mersenne in this article. I presume he's a person with his own article? 2 - I got to Mersenne Prime via clicking a link to a Mersenne Number. Does Mersenne number derserve its own article? 3 - Shouldn't there be some mention somewhere of the fact that a mersenne number in binary is of the form 11111<...>111? Manning 06:25, 4 January 2007 (UTC)
Would someone good at number theory like to rewrite my proof of 3) to get rid of all my group theory crutches and make it more leisurely and explanatory? Thanks, Rich 05:35, 21 February 2007 (UTC)
http://primes.utm.edu/glossary/page.php?sort=MersennesConjecture
n the preface to his Cogitata Physica-Mathematica (1644), the French monk Marin Mersenne stated that the numbers 2n-1 were prime for
n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257
Yet the list is as follows:
# | p | Mp | Digits in Mp | Date of discovery | Discoverer |
---|---|---|---|---|---|
8 | 31 | 2147483647 | 10 | 1772 | Euler |
12 | 127 | 170141183…884105727 | 39 | 1876 | Lucas |
Should not Mersenne be credited for those two? Alex 68.46.132.117 ( talk) 05:25, 3 February 2010 (UTC)
No, he merely conjectured that 2p-1 was prime for those values, getting two of his four unproved guesses (for p = 67 and 257) incorrect and missing three more (p = 61, 89 and 109). Euler and Lucas actually proved that the above two (p = 31 and 127) were prime. The first seven on his list had already been discovered so don't really count. -- Glenn L ( talk) 07:01, 3 February 2010 (UTC)
Anonymous user 74.3.4.112 noted the following Google Group message:
However, when I tested M86243 on Prime95, I got: "M86243 is Prime! Wd1: 82145A39,00000000"
Although 1,627,710,365,249 = 86,243 * 18,873,536 + 1 and therefore could qualify as a factor, I am very suspicious.
-- Glenn L 11:56, 16 May 2010 (UTC)
The number of digits of a mersenne prime is approximately equal to its log base 10, since the number of digits of any number, prime or not, is the one more than the integral part of its log base 10. For example, log(base 10) of 10 is 1, while log(base 10) of 100 is 2.
That the number of digits in a mersenne prime is approximately 30% of its exponent follows from the fact that 2**10 = 1024 ≈ 1000 = 10**3. 10% of the exponent gives the number of 1000's, and three times that gives the number of digits. :-) ( Martin | talk • contribs 05:10, 27 April 2010 (UTC))
Please comment on the following valid and important point which has been deleted from the text:
The international inch is defined to be equal to exactly 2.54 centimeters, or equivalently 1 in = 127/50 cm. Thus the Mersenne prime M7=127 enters conversion between the United States customary units and the International System of Units (SI, often referred to as "metric").
Arcshinus ( talk) 02:32, 7 October 2010 (UTC)
The British-American system of units is still widely used because of historical traditions and industrial machining tools. The system's units such as hand, foot, yard, and fathom are derived by multiplying inch by prime factors 2 and 3 while pace, rod, furlong, and mile introduce prime factors 5 and 11. On the other hand the units in the decimal International System are derived by multiplying by powers of 10 (prime factors 2 and 5). It is remarkable that the conversion between the two system was "rounded" in such a way that a new prime factor 127 appeared. The round-off error distribution statistics is greatly affected by what factors are used in conversion between the systems. So the issue here is more subtle than just being some number. —Preceding unsigned comment added by Arcshinus ( talk • contribs) 02:50, 9 October 2010 (UTC)
In the image of the graph showing the digits in the largest known Mersenne prime, why is this graph a line? Shouldn't it be only points at the corresponding points in time when a Mersenne prime was discovered? This way it looks as if new Mersenne primes are continously being discovered, which obviously isn't the case. Toshio Yamaguchi ( talk) 14:17, 4 December 2010 (UTC)
The section "Generalization" seems like it wants to mention the article on repunit primes, but it doesn't do it. It seems like this deserves a note in another section (perhaps "About Mersenne primes"?), but doesn't warrant its own section. Andypar ( talk) 05:05, 27 January 2011 (UTC)
Mersenne 48 and 49 at OEIS. I have done (in Mathematica) LLT and this:
Select[Range[10^3], PrimeQ[2^# - 1] &]
Martin Sojournerfix ( talk) 19:25, 10 March 2011 (UTC)
? Mod(2,349958939111)^43581437-1 %1 = Mod(0, 349958939111) ? Mod(2,100313477119)^49318327-1 %2 = Mod(0, 100313477119)
? Mod(2,5789358091081)^43581437-1 %3 = Mod(0, 5789358091081)
Article states: It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes.
If p is a SG prime and ≡ 3 (mod 4), 2p + 1 will indeed divide 2^p - 1, but if p ≡ 1 this is not true! 89 is SG and 2^89 - 1 is prime. Hence, the claim in the paragraph cited is in error; you need the stronger fact that there are infinitely many SG primes ≡ 3 (mod 4). —Preceding unsigned comment added by 213.67.74.59 ( talk) 23:51, 16 April 2011 (UTC)
I am unsure if this section is appropriate per MOS:MATH#Proofs and I added a cleanup template. The section gives no information about the importance or any other contextual information. I welcome comments from other editors. Toshio Yamaguchi ( talk) 17:11, 5 May 2011 (UTC)
I added the citation for Euclid's theorem about Mersenne primes and perfect numbers. He phrases it thus: "If as many numbers as we please beginning from an unit be set out continuously in double proportion, until the sum of all becomes prime, and if the sum multiplied into the last make some number, the product will be perfect." The opening "if" is equivalent to "if we add 1+2+4+8+... to any number of terms", which is another way of saying (...1111) in binary. No idea how to track down Euler's contribution. Grommel ( talk) 03:24, 5 June 2011 (UTC)
I was surprised that my change of "Ancient Greek mathematicians" to "Pythagoras and/or other ancient Greek mathematicians" respective to "Euclid and/or other ancient Greek mathematicians" was reversed and even called "vandalism". The first ancient Greek mathematicians refered to in this case is Pythagoras who was the first known author speaking about "prime numbers" and mentioning 3 and 7 as prime numbers. The second "ancient Greek mathematician" is Euclid who in his book Elementa is the first to mention perfect numbers, which is also mentioned in the wikipedia article on Euclid. Euclid also mention 31 and 127 in the context of perfect numbers. Of course you can argue that it is uncertain what was written by Pythagoras and Euclid. Writings which have their name could have been written by others. It is even uncertain if there ever existed any living persons like "Pythagoras" and "Euclid", or at least someone can question it. If you go to your book shelf though and look up the specific writing where 3 and 7 are mentioned as prime numbers for the first time, this book has the name "Pythagoras" on the cover and if you go for the book where perfect numbers are mentioned for the first time this book is called "Elementa" and has the name "Euclid" on the cover. So I think it is a legitimate opinion to think that their names should be added to the article on Mersenne primes and I disagree with calling it "vandalism". — Preceding unsigned comment added by 193.11.50.158 ( talk) 15:05, 19 September 2012 (UTC)
When quoting sources a source closer to the actual historical happening is considered better. Nowadays it is often possible to see the traces, relicts, from an occasion on the internet since it is still there.
GIMPS (Global Internet Mersenne Prime Search) is a distributed search for Mersenne primes using softwares like prime95. The computer programs are running on the participants computers and whenever there is a result/output it is sent to a server (primenet-server), where the result is included in the log-file and database. In the GIMPS pressrelease concering Mersenne primes number 45 and 47 it is not mentioned which dates they were found. Fortunately on the user forum, mersenneforum.org, the logfiles (with the faked LL-residues) are quoted: logfile M#45 found on "06-Sep-08 19:53" UTC and logfile M#47 found on "23-Aug-08 7:33" UTC.
All other sources to when these Mersenne primes were found are directely of indirectely based on the information in the logfiles, hence a primary source or relict. 83.216.98.37 ( talk) 17:35, 9 October 2012 (UTC)
Quite some time ago the date for the find of Mersenne prime #30 was changed from "September 20 1983" to "1983 September 19" and for #31 from "September 6 1985" to "1985 September 1" without giving any reliable sources for these changes. So far I have not been able to find any conclusive arguments for which of the dates are correct. The oldest and, as it appears, most reliable sources have "September 20 1983" and "September 6 1985" respectively, but I don't like to make any changes until I feel I can prove which is right especially since I don't know on which ground the changes were made.
Well, this is just to let you know that I am working on this. Any help is appreciated. 193.11.50.158 ( talk) 10:01, 21 September 2012 (UTC)
Speusippus, c. 408 – 339/8 BCE, wrote a book named On Pythagorean Numbers. This book was mainly based on the work of
Philolaus, c. 470–c. 385 BCE, according to
Iamblichus, c. 245–c. 325 CE, who obviously had access to both the book of Speusippus and the work of Philolaus and could compare their works. Iamblichus gives us a long, direct quotation of Speusippus and in this quotation we find the oldest known reference to the concepts of prime numbers and composite numbers. It is clear of course that since Philolaus knew about (or "discovered") prime numbers he also knew about the smallest ones like 2, 3, 5, 7, 11.
So why do I also like to include the following passage of the quotation from Speusippus: "Ten does have an equal amount /.../ it is the first in which an equal amount of incomposite [i.e. 1,2,3,5,7] and composite [i.e. 4,6,8,9,10] numbers are seen. /.../ seven is a multiple of none"?
If we take the easiest part first: "seven is a multiple of none", that is a different way of saying that "7 is a prime number". It would be nice to include it since it is the first time ever in the history of numbers that 7 is said to be a prime number. Yes, I only like to quote that small part since its a part of a larger discussion which would only obscure things if we quote.
OK, number 3 then? Is there any reference to number 3 as a prime number. Well, once again if you know that there are prime numbers surely you know that 3 is a prime number. Beside that, in the passage I like to quote, we find a discussion about why 10 is to be recognized as a "perfect number" and here we are not talking about "perfect number" in a modern sense, but the old Greek mathematicians were thinking about numbers with good quality, ideal numbers. So, Iamblichus and my interpretation of Philolaus (according to Speusippus) is that, one of the arguments why 10 should be called a "perfect number" is that among the 10 numbers less than and equal to 10 (1, 2, 3, 4, 5, 6, 7, 8, 9 and 10) we find an equal amount of prime numbers and composite numbers "it is the first in which an equal amount of incomposite and composite numbers are seen." The prime numbers (incomposite) referred to here must be 1, 2, 3, 5 and 7. The composite numbers must be 4, 6, 8, 9 and 10. So, the conclusion from this passage is, even if it is an implicit reference, that Philolaus knew that 3 and 7 are prime numbers.
So the reason why I also want to include these two parts of the quotation:
A. "Ten does have an equal amount /.../ it is the first in which an equal amount of incomposite [i.e. 1,2,3,5,7] and composite [i.e. 4,6,8,9,10] numbers are seen."
B. "seven is a multiple of none"
is that they give a direct reference to the numbers 3 and 7 as prime numbers and its the first time ever they are said to be prime numbers.
83.216.101.203 (
talk)
09:57, 25 November 2012 (UTC)
The few edits that as of now trickled are only a tiny start. Expect a large flood. I suggest to lock article until Tue, Feb 5th (which is known to be the date of the official press release), to save your reverting efforts.
Additional page to consider locking is the "Largest_known_prime_number". — Preceding unsigned comment added by 99.121.250.148 ( talk) 20:10, 1 February 2013 (UTC)
Regarding M48 which has recently been added, it is being discussed here. Here it is claimed primality has been verified. -- Toshio Yamaguchi 11:09, 27 January 2013 (UTC)
It has not yet been added to the milestones list though. -- Toshio Yamaguchi 11:23, 27 January 2013 (UTC)
The definition of the article's subject does not appear until the second paragraph of the lead. Wouldn't it be less confusing to start with "A Mersenne prime is a prime number of the form 2^n - 1" and go from there, pointing out that (a) n is necessarily prime and (b) (by back formation?) a number of the form 2^n - 1 is called a Mersenne number? -- Vaughan Pratt ( talk) 17:59, 4 February 2013 (UTC)
The Infobox integer sequence at the top of the article is confusing: it looks like Ulrich Regius published on Mersenne primes before Mersenne was born. While this is true, there should be something in the History section to clarify. I'm not knowledgeable enough, but this should be easy for someone who is. By the way, is there an English translation of Regius' work? A Wikipedia article on Regius? I couldn't find either. Myron ( talk) 13:56, 6 February 2013 (UTC)
This may be a dangerous question to pose, but it would be nice to know (ie. add to article) what practical use is or can be made of Mersenne numbers, if any. I get that the search is 'fun' (fsvo) in itself but are there specific use cases for this series of numbers? -- AlisonW ( talk) 22:48, 7 February 2013 (UTC)
I noted there is some inconsistency in the representation of the numbers in this article. For example long numbers in Mersenne prime#History and Mersenne prime#Factorization of composite Mersenne numbers use comma separated digit groups, while the numbers in Mersenne prime#List of known Mersenne primes don't use commas. Wikipedia:Manual of Style/Dates and numbers#Delimiting (grouping of digits) says numbers with five or more digits should be separated into groups using commas and also says that in scientific articles thin spaces can be used instead. Which style should be used in this article? I suggest to apply that style to all numbers in this article, after an appropriate one has been identified. -- Toshio Yamaguchi 15:14, 9 February 2013 (UTC)
The text there matches from this reference: 1. It may or may not be appropriate here but would need a citation at the least. (I researched it because of the edit mark at the start of the section made May 2011].-- Billymac00 ( talk) 00:53, 11 February 2013 (UTC)
It can be easily seen that if p is an odd prime, then 2p - 1 ≡ 7 or 31 (mod 40). It can be easily proven that 2p - 1 ≡ 7 or 11 (mod 20). This is because 2p - 1 ≡ 3 (mod 4) and 2p - 1 ≡ 7 or 1 (mod 10). So, in the case that 2p - 1 ≡ 7 (mod 10), 2p - 1 ≡ 7 (mod 20) since for all integers k, 20k + 7 ≡ 3 (mod 4) and 20k + 17 ≡ 1 (mod 4) ≠ 3 (mod 4). In the case that 2p - 1 ≡ 1 (mod 10), 2p - 1 ≡ 11 (mod 20) since for all integers k, 20k + 11 ≡ 3 (mod 4) and 20k + 1 ≡ 1 (mod 4) ≠ 3 (mod 4). However, I need someone to go further and prove that 2p - 1 ≠ 11 or 27 (mod 40). This is a necessary condition to prove that 2p - 1 ≡ 7 or 31 (mod 40). PhiEaglesfan712 15:52, 13 July 2007 (UTC)
The 3rd reference is a dead link. Blackbombchu ( talk) 03:29, 4 December 2013 (UTC)
Sometimes Wikipedia has 2 different ways to write an article an despite that neither of them is enforced throughout the entire Wikipedia system, each individual article is supposed to pick only one of the 2 styles to stick to and not mix them, for example Wikipedia's policy doesn't allow a ship to be refered to as it in one part of an article and she in another part of the same article. For consistencey, since most of the mathematical expressions that are not not their own sepearte line are using html code, I think the rest of the mathematical expressions in the article that are not on their own separate line should also be switched from latex to html code. Furthermore, I know the html code for those expressions really well so I should be the one to make that change. Is it fine for me to make that change, only for the ones that are not by themselves on a line? Blackbombchu ( talk) 20:40, 7 December 2013 (UTC)
2P-1 is an odd number ⇒ 2P-1 ≡ 1(mod 2)
By Fermat's little theorem, we see that, 2P ≡ 2(mod p) ⇒ 2P-1 ≡ 1(mod p)
if p is an odd prime then: 2 ≡ -1(mod 3) ⇒ 2P ≡ (-1)P(mod 3) ⇒ 2P-1 ≡ -2(mod 3) ⇒ 2P-1 ≡ 1(mod 3)
So we got:
2P-1 ≡ 1(mod 2)
2P-1 ≡ 1(mod 3) ... ( for p>2 )
2P-1 ≡ 1(mod p)
So, for p>3 , we can found that 2P-1 ≡ 1(mod 6p)
Note: 2P-1 doesnt have to be a prime number!
Isaac.mor (
talk)
08:30, 24 October 2014 (UTC)
Mn = 2n-1
its well known that you can build Mn digits using only the digits of n
lets show a few examples:
if the last 2 digits of n are ....17 then Mn last 3 digits have to be ....071
if the last 2 digits of n are ....23 then Mn last 3 digits have to be ....607
i will only show the roles for an odd n because we wanna use it for primes
| or |
|
just so you know the same works for 3 digits of n lets show a few examples:
2... 639-1 = 2... 139-1 = ... 1887
2... 711-1 = 2... 211-1 = ... 8047
etc ...
the same works for any k digits of n
but for really big numbers you need a LOT of computer power :)
Isaac.mor (
talk)
12:03, 24 October 2014 (UTC)
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Cheers. — cyberbot II Talk to my owner:Online 03:57, 27 August 2015 (UTC)
A new Mersenne prime was discovered on Jan. 07 2016. See http://www.mersenne.org/primes/. This calls for a substantial edit to this page as well as many other wikipedia pages, because "largest prime", "second largest prime", and "largest mersenne prime" are used extensively referring to now-incorrect numbers.
66.31.237.80 ( talk) 05:34, 24 January 2016 (UTC)
I think the graph in the article is wrong. There is a slow increasing line between 1950 -1960 indicating every year a bigger Mersenne prime was found with an increase in size equal to the previous each year, then between approx. 1960 -1962 for two years the rate increased. in my opionion there should be horizontal lines between discoveries of the finds and no steady increase. for the last few years it does not matter that much as the rate of finds are increased so much that the graph will be about the same (i think the point of the graph) 195.240.149.123 ( talk) 04:30, 13 August 2010 (UTC)
I freely admit to not being a mathemetician, or indeed particularly number-savvy with regard to primes, but there is an inconsistency in the article with regard to the number 2. Within the confines of this article, is "2" considered a Mersenne prime? Part of the article suggests it is, and part not.
In the history section, 2 is listed as a prime (and the section states that "His list was accurate through 31",) and the image includes 2 as a Mersenne prime, yet the rest of the article - especially the lede: "The first four Mersenne primes (sequence A000668 in the OEIS) are 3, 7, 31, and 127." - doesn't include 2.
I see that there is reference to two different OEIS sequences - one of which includes 2, and one that doesn't, however this is confusing to those who don't have an in-depth understanding of the subject matter. In short - as it currently stands the article is inconsistent, and should:
( talk) 06:28, 1 January 2017 (UTC)
Not yet, but now that it's been explained to me, I'll certainly think about. I solidly fall into the "not fluent" category, and it puzzled the hell out of me. Chaheel Riens ( talk) 18:29, 1 January 2017 (UTC)
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Does anyone understand what [27] means? It's not a minor edit, it's unsourced, it's been undone by four different editors, and User:PrimeHunter has been unable to find anything about the claim [28]. Meters ( talk) 04:28, 3 December 2017 (UTC)
It is not a claim, it is a fact that is useful for generating pyramid charts. You wont find out by googling it, you will find out by doing it. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 04:42, 3 December 2017 (UTC)
Your right, it is not a good idea for you, but it is a good idea for the page. As a great man once said, "if you cannot see what is right in front of you then you are indeed a fool." Please physically investigate this for yourself before any further complaints. this is a useful addition not a reckless destruction, so please do not treat it as such. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 04:47, 3 December 2017 (UTC)
Please stop the vadalism, or i will have to email wikipedia about this. i am making a valid useful contribution anyone who checks it out for themselves will understand on be on my side. i cannot provide a source for nature and basic geometry so i am sorry, but your just going to have to use your eyes and brains. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 04:58, 3 December 2017 (UTC)
If i get blocked than that just proves that wikipedia is a useless pile of rubbish and that indeed the vast majority of people are in fact not intelligent at all, but petty belligerent fools. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:07, 3 December 2017 (UTC)
wikipedia, a pun for world wide web encyclopedia. encyclopedia, a book giving information. My addition is information that is immediately verifiable and self evident, and is therefore viable information. how is Wikipedia ever to improve if it seeks to remove and destroy basic facts? then it would be called wikibook. so i am sorry but you are all wrong. please read my addition more carefully, try it for yourself and ponder it for at least a day before even thinking about removing it as the is no logical or reasonable basis for doing so. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:23, 3 December 2017 (UTC)
PLEASE STOP UNDOING! there is no need to. it does not change anything, it only adds an additional valid & verifiable point, which is in the spirit of wikipedia. It is a description of an image therefore it require no citation. please read and understand the rules before attempting to enforce them. — Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:28, 3 December 2017 (UTC)
PLEASE STOP UNDOING! there is no need to. it does not change anything, it only adds an additional valid & verifiable point, which is in the spirit of wikipedia. It is a description of an image therefore it require no citation. please read and understand the rules before attempting to enforce them. Draw a pyramid chart, count the spacing, if you still do not understand than i don't think you have any authority to undo it, because you obviously don't understand it therefore have no right to comment.— Preceding unsigned comment added by Kulprit001 ( talk • contribs) 05:30, 3 December 2017 (UTC)
@
Kulprit001:, the belligerent and pig-headed way you approached this discussion was always doomed to failure: Wikipedia works on a collaborative model, and if you can't explain to others what you're doing politely then it will never work. That being said, @Everyone else: Kulprit is almost certainly trying to express that the number of nodes in a full (or complete) binary tree with n layers is the Mersenne number 2^n - 1. (Or something equivalent.) This is a totally true thing. And in fact Mersenne numbers are a common answer to lots of enumerative combinatorial questions, although they aren't usually called "Mersenne numbers" in that context. It is a reasonable question about whether these combinatorial facts should be listed somewhere, either in the section Kulprit was trying to add to, or in a separate subsection called "in enumeration" or something. --
JBL (
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14:37, 3 December 2017 (UTC)
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I removed the following text from the introduction:
and this from "Mersenne numbers in nature":
Both are based on the belief that a Mersenne number is 2n−1, which is a mistake. The correct "pernicious" part is that there be a prime number of 1's followed by a large number of 0's that seems too trivial to bother mentioning (especially in an introduction). Zaslav ( talk) 04:13, 6 October 2018 (UTC)
The section about "primitive part" is impossible to understand to the largest part of it. For example,
The phrase is grammatically incorrect and incomplete, and it is not clear what the author wanted to say. It's similar for the whole subsection and a later one, probably from the same "contributor". Is anyone please willing to improve this? Such "contributions" are annoying, the article would be better without it. I'd suggest to move the subsection here (i.e., delete it from the main page) until it is rewritten in correct English. As it stands, it barely qualifies for a comment on this talk page. But I don't know whether doing so is (WP-)"politically correct". — MFH: Talk 17:48, 5 December 2018 (UTC)