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Archive 5 | Archive 6 | Archive 7 | Archive 8 | Archive 9 |
Add prime number 343 to list of primes. — Preceding unsigned comment added by 95.49.26.86 ( talk) 11:57, 5 July 2014 (UTC)
[1] It is a mystery why anyone would turn up on this talk page and say that low value prime numbers are missing, because all of the primes in this range were discovered a long time ago. It is possible, however, that there are non- Mersenne primes in between the very large ones that have been discovered by computer.-- ♦IanMacM♦ (talk to me) 19:52, 7 July 2014 (UTC)
Is there a generally agreed on definition of a rational prime number? 173.79.197.184 ( talk) 13:08, 1 August 2014 (UTC)
Third to last paragraph in History should not ignore Miller-Rabin: http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html. Still the gold-standard test for speed and practicality. 19:33, 7 August 2014 (UTC)
This really is the most basic element of prime distribution. I don't understand why anyone would want to hide this very basic and important fact about primes. As I said: "The 6n±1 is the most primary filter, and is basic to all elementary introductions to primes. This 2/3 filter does NOT exist in any other mod that isn't a multiple of six. If you want to describe the 6n±1 concept in another way, go for it." This is probably more important and basic than most everything else on this page. Why would you want to delete it? Again, if you don't like the way I've illustrated the 6n±1 concept, feel free to improve upon it. But deleting it is just plain weird... TurilCronburg ( talk) 20:48, 19 July 2014 (UTC)
Wolfram includes it in their Prime Number write-up. 67.188.92.176 ( talk) 20:05, 10 August 2014 (UTC) Robin Randall, Aug 2015
This sort of thing is literally as basic as it gets. It's the kind of thing you'd see on an elementary school level discussion of primes. For example: http://primes.utm.edu/notes/faq/six.html which is the prime FAQ on a kid's math website. This fact about primes is kind of the equivalent of saying that atoms are made up of protons, neutrons, and electrons. TurilCronburg ( talk) 21:26, 19 July 2014 (UTC)
An observation, particularly directed at TurilCronburg: one reason that your contribution is meeting resistance is that it is misplaced. When mathematicians speak of "the distribution of primes", they are not generally speaking about modular identities (like, e.g., the fact that all primes other than 2 are odd). Instead, the phrase "distribution of primes" relates to questions like "what is the probability that a randomly selected 10-digit integer is prime?" Reasonable answers to this question are very hard, and require sieving by larger and larger sets of primes; meanwhile, for any finite collection of primes it is easy to write down a modular sieve of exactly the sort you are describing. I agree with you that the mod 6 sieve is more appealing than a random example of such a thing; it is totally plausible that one could find some interesting history on the use of this sieve and slot a paragraph about it into this article or a related one. But, the place you are putting this paragraph is definitely wrong.
It may help you to imagine what would happen in the future were some other editor to come and insist that we include mention of the important and fascinating fact that every prime number is congruent to plus-or-minus 1,2,4,7,8,...,37 mod 75. How should someone explain to this editor (who has a deep and abiding personal belief in the importance of this fact) why it does not belong in the section on distribution of prime numbers? Best, JBL ( talk) 18:47, 26 July 2014 (UTC)
For Quantum connection to zeta function could it be referring to the Casimir Effect? 67.188.92.176 ( talk) 20:05, 10 August 2014 (UTC)Robin Randall, Aug. 2014
"There is no known useful formula that sets apart all of the prime numbers" - is there a useless one? What does "useful" mean? Are there formulas that require computing power beyond our abilities? -- Richardson mcphillips ( talk) 17:52, 6 February 2015 (UTC)
Under "number of prime numbers below a given number" section, you might want to add the derivative of pi(n) n/ln(n) which is [ln(n)-1]/[[ln(n)]^2], which gives the approximate fraction of prime numbers at a certain 'size' number. For example, at the 1,000,000,000 level, you can expect about 46 out of 1000 numbers to be prime. 71.139.161.9 ( talk) 19:37, 7 September 2014 (UTC)
It seems like someone forgot to have a section on the Interval Containing At Least One Prime Number. So, I will suggest it. John W. Nicholson ( talk) 17:55, 1 March 2015 (UTC)
The article claims that the latest prime number was found in April 2014 and later in the sentence links to the wikipedia list of largest prime numbers. However, that article claims that the latest largest prime number was discovered in February 2013. 216.96.200.76 ( talk) 16:13, 14 April 2015 (UTC)
" ...the probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n."
To me this seems to be saying that any two digit number has a 50% chance of being prime, a three digit number has a 1 in 3 chance, etc. Obviously, that's not the case.
Am I just misreading it? — Preceding unsigned comment added by Tym King ( talk • contribs)
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I believe my addition of : "non-prime numbers (or rather, their factorization) can be said to be 'composed' of the primes themselves" has merit, as it makes clear the explanation that immediately follows it. Can we not leave it in? — Preceding unsigned comment added by Baguettes ( talk • contribs) 21:57, 26 September 2015 (UTC)
Again, I am confused when it says pi(11) = 5 for the 5 primes LESS THAN OR EQUAL to 11. Later it appears pi(n) represents the number of primes LESS THAN the number N. Which is it? Or does the approximate operator take care of this? RobinLRandall 15:01, 15 Oct 2015 (UTC) — Preceding unsigned comment added by 67.188.92.176 ( talk)
I just removed a reference to Mathworld regarding the fact that Euler did not consider 1 as a prime number, and replaced it by a direct reference to one of Euler's theorems, from which statement this fact is clear. In fact Weisstein's reference only mentioned that Goldbach considered 1 to be a prime, and not that Euler did not. But this is beside the point. I think we should generally avoid references to Weisstein's online encyclopedy, which is not reliable at all as it contains many approximate and false informations. It has the same disadvantages as Wikipedia has (of having subjects treated by non specialists), with the further drawback of being edited by essentially one single non specialist - Weisstein himself. Sapphorain ( talk) 08:02, 18 November 2015 (UTC)
There has been some recent edit/reversion going on. My feeling is that it would be nice to mention the AKS algorithm (or some other aspect of algorithmics) in the paragraph in question, but that the level of technicality should be kept to the level "could be understood with a high school education." I suggest discussing the text here in order to reach consensus, rather than continuing to edit the article directly. -- JBL ( talk) 22:21, 5 November 2015 (UTC)
The AKS algorithm, which is considered very slow for practical sizes, shows that deciding whether a number n is prime has polynomial complexity, which means that in the general case it can be done quickly. For practical sizes, probabilistic algorithms such as the Miller-Rabin algorithm are preferred, which execute very fast at the cost of some small error probability.
Hi, this is a ridiculously minor thing, but I think the word "surprisingly" should be deleted from the bit about Ulam spirals clustering on certain diagonals, so as to maintain an objective tone. — Preceding unsigned comment added by 140.233.173.75 ( talk) 10:00, 18 December 2015 (UTC)
I'm just a random passer-by, but want to point out that the statement below on the page, about the prime number theorem, is not correct:
... , which says that the probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n.
The prime number theorem defines \pi(x) as the number of primes less than x, and says that is \pi(x) is proportional to log(x).
It says that the probability that a number n chosen at random from [2 ... x] is prime, is proportional to y = log(x).
This is not the same thing as the number of digits of n, the number that was chosen at random. The probability that a random number of exactly n-digits is prime, is proportional to something like \pi(10^n) - \pi(10^n-1). You have to cut out all the numbers that have fewer digits from the pool. — Preceding unsigned comment added by Ccmxxx ( talk • contribs) 16:18, 26 December 2015 (UTC)
My edit has been reverted, restoring the following wording:
True, the m=1 case is just a null product. But the point of my edit was that the old and restored version claims that (m, n)=(1, 0) or (1, 1) gives the number of sides of a constructible regular polygon: a1-sided polygon and a 2-sided polygon respectively. The former is impossible, and the latter is possible only if we admit a degenerate polygon. So I think the wording needs to be corrected. Loraof ( talk) 21:12, 15 March 2016 (UTC)
This article and Euclid's theorem attribute different proofs of the infinitude of primes to Euler. This one says it's about the divergence of the series of prime reciprocals, while the other one involves an Euler product formula for the harmonic series. Are they both Euler's? Shouldn't we be more consistent? — David Eppstein ( talk) 21:48, 17 March 2016 (UTC)
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Number of prime numbers
Prime Numbers Set Definition
Definition of prime numbers can be written all over as this: Prime numbers does not have a factor other than itself and 1; as following;
Sets consists of 's are;
Thus;
P shows prime numbers' set,
Some features of sets are like below,
Set A consists of positive integers starting from 1, set B consists of positive integers greater than 1. Separately multiplying their own members with their own thus getting a new pair of sets. The difference of the new sets is the set of almost prime numbers. 1 is not a member of the prime numbers' set, prime numbers' set could be obtained by substracting 1 from latest found set. If it's desired a N value could be selected by that prime numbers' set can be obtained within the range of 1 to N -- Nexusiot ( talk) 20:46, 2 June 2016 (UTC) Comment : "Please add this new feature" -- Nexusiot ( talk) 20:46, 2 June 2016 (UTC)
Nexusiot ( talk) 20:46, 2 June 2016 (UTC)
All prime numbers have to follow this formula is: 6n±1 — Preceding unsigned comment added by 212.253.111.210 ( talk) 00:33, 5 October 2016 (UTC)
Best regards
Nedim ERDAN — Preceding
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In the list of prime number you have 101 as a prime number, this is incorrect. — Preceding unsigned comment added by Theisencouple ( talk • contribs)
The largest known proth prime in Prime_number#Special-purpose_algorithms_and_the_largest_known_prime is not up-to-date, see also Seventeen or Bust. Due to the protection of the article I can't update it myself. Der Waldkauz ( talk) 12:49, 3 January 2017 (UTC)
I think will be time to give a math definition of primes that match as possible the "talking of" definition:
is a prime if and only if:
This definition respect the known one in the main concept of Prime as result of a recursive division, missing just 2.
From the definition fits for all Naturals.
Usinig this definition and 2 algos involving Sums / Product / Fractions and Integer part of..., it's possible to count the primes and given one find the next one. This algos are of course not computable immediately from very little primes due to factorial product, but in theory they give a perfect definition of Primes as well sorted numbers. So pls delete elsewhere the phrase "we actually don't know if primes are well sorted or not...".
Stefano Maruelli — Preceding unsigned comment added by StefanoMaruelli ( talk • contribs)
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Please add in the References section the information about my new book. [1] Please add in the External links section the link-information about my new book (hope this is correct, because this is my first post ....) <ref prime numbers - new results </ref> Karl-Heinz Kuhl ( talk) 09:33, 22 January 2017 (UTC) Karl-Heinz Kuhl ( talk) 09:33, 22 January 2017 (UTC)
References
article states
It consists of testing whether n is a multiple of any integer between 2 and the square root of n.
for the number 1,999,999 this is not true... the square root of 1,999,999 is 1414.xxx... but the factors of 1,999,999 are 1657, 71, 17... since 1657 is greater than 1414 then 1,999,999 would be considered prime... but it is not... trust this helps I do not know how to sign this Dan Ellwein 2601:3C5:4202:313D:9D48:94A6:1D00:E135 ( talk) 05:34, 8 February 2017 (UTC)Dan Ellwein 2601:3C5:4202:313D:9D48:94A6:1D00:E135 ( talk) 05:34, 8 February 2017 (UTC)— Preceding unsigned comment added by 2601:3C5:4202:313D:9D48:94A6:1D00:E135 ( talk) 05:27, 8 February 2017 (UTC)
Why does the article say that primes are natural numbers? I think this is a serious missinformation. Why are the negative primes not included in presentation?-- 82.79.114.5 ( talk) 08:42, 22 February 2017 (UTC)
My math isn't great and I'm falling asleep, but the prime number article says:
The fundamental theorem of arithmetic article seems to disagree (see the part of this quote I bolded):
I think the prime number article is missing an important part of that sentence. 3 is an integer greater than 1; if 1 is not a prime number, how can 3 be expressed as a product of primes?
So... Yeah. Thank you and good night. 71.121.143.38 ( talk) 08:10, 30 March 2017 (UTC)
I found a great article from the Institute for Advanced Study that I thought might could contribute some to the prime number article!
https://www.ias.edu/ideas/2013/primes-random-matrices — Preceding unsigned comment added by 2001:4642:11C6:0:5D:4668:A89:EB74 ( talk) 18:28, 1 July 2017 (UTC)
For a long time, when all the prime numbers up-to some given number were evaluated, it was expected that its 'distribution'/'count off' must/can be represented by a simple analytical function. The distribution of prime numbers is indeed be a pattern related phenomenon but the means that pattern has been sought is misguided/ill-advised, according to Yoldas Askan, a British scientist and mathematician. In his paper, Yoldas challenges some of the fundamental understanding of Prime Numbers and reconsiders these definitions, and ultimately arrives at his analytical formula. In his view, there is no great deal about functions that are approximations because there can be infinitely many of these derived but only suitable at certain number interval. Yoldas claims that the 'beautiful' thing about the Prime number distribution is that there will be no analytical function [of any complexity] that will compute and provide exact values for π(x) other than the Prime Number Distribution Series, which is provided as follows, — Preceding unsigned comment added by Nuclearstrategy7 ( talk • contribs) 17:37, 14 July 2017 (UTC)
This has languished on the ArXiv for very long without actually being published – presumably because it is apparently so long that Helfgott's website lists it as to appear as a standalone book. Mind you, if it had not already long since been checked and accepted, one wonders why he got the Humboldt professorship specifically for it. Double sharp ( talk) 13:23, 17 July 2017 (UTC)
I have requested comments at Wikipedia talk:WikiProject Mathematics. Double sharp ( talk) 14:01, 17 July 2017 (UTC)
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There is a new theory is called ASA method, gives a solution to the prime numbers in generation and distribution, Read the published Paper -- Alsumery2 ( talk) 22:24, 2 September 2017 (UTC)
The discussion has become meaningless and sterile Some users are not specialists who are not worthy of the subject-matter evaluations, leaving the subject and going beyond the core of the research is unfortunate Alsumery2 ( talk) 15:28, 3 September 2017 (UTC)
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In the "Special-purpose algorithms and the largest known prime" section, it says:
For example, the Lucas' primality test requires the knowledge of the prime factors of n − 1, while the Lucas–Lehmer primality test needs the prime factors of n + 1.
I believe the second link is a typo and should point to some other page. The article for the Lucas-Lehmer test does not suggest that it needs the prime factors of n + 1. Unfortunately, I don't know which article link should be put in its place. The article for the Lucas test does not provide a mention of its n + 1 counterpart. Additionally the MersenneWiki page on primality tests lists only one test that needs the factors of n + 1, calling it "Morrison's Theorem," but the link is dead and I can't find a reference to this theorem online. Derek M ( talk) 23:01, 7 January 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 5 | Archive 6 | Archive 7 | Archive 8 | Archive 9 |
Add prime number 343 to list of primes. — Preceding unsigned comment added by 95.49.26.86 ( talk) 11:57, 5 July 2014 (UTC)
[1] It is a mystery why anyone would turn up on this talk page and say that low value prime numbers are missing, because all of the primes in this range were discovered a long time ago. It is possible, however, that there are non- Mersenne primes in between the very large ones that have been discovered by computer.-- ♦IanMacM♦ (talk to me) 19:52, 7 July 2014 (UTC)
Is there a generally agreed on definition of a rational prime number? 173.79.197.184 ( talk) 13:08, 1 August 2014 (UTC)
Third to last paragraph in History should not ignore Miller-Rabin: http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html. Still the gold-standard test for speed and practicality. 19:33, 7 August 2014 (UTC)
This really is the most basic element of prime distribution. I don't understand why anyone would want to hide this very basic and important fact about primes. As I said: "The 6n±1 is the most primary filter, and is basic to all elementary introductions to primes. This 2/3 filter does NOT exist in any other mod that isn't a multiple of six. If you want to describe the 6n±1 concept in another way, go for it." This is probably more important and basic than most everything else on this page. Why would you want to delete it? Again, if you don't like the way I've illustrated the 6n±1 concept, feel free to improve upon it. But deleting it is just plain weird... TurilCronburg ( talk) 20:48, 19 July 2014 (UTC)
Wolfram includes it in their Prime Number write-up. 67.188.92.176 ( talk) 20:05, 10 August 2014 (UTC) Robin Randall, Aug 2015
This sort of thing is literally as basic as it gets. It's the kind of thing you'd see on an elementary school level discussion of primes. For example: http://primes.utm.edu/notes/faq/six.html which is the prime FAQ on a kid's math website. This fact about primes is kind of the equivalent of saying that atoms are made up of protons, neutrons, and electrons. TurilCronburg ( talk) 21:26, 19 July 2014 (UTC)
An observation, particularly directed at TurilCronburg: one reason that your contribution is meeting resistance is that it is misplaced. When mathematicians speak of "the distribution of primes", they are not generally speaking about modular identities (like, e.g., the fact that all primes other than 2 are odd). Instead, the phrase "distribution of primes" relates to questions like "what is the probability that a randomly selected 10-digit integer is prime?" Reasonable answers to this question are very hard, and require sieving by larger and larger sets of primes; meanwhile, for any finite collection of primes it is easy to write down a modular sieve of exactly the sort you are describing. I agree with you that the mod 6 sieve is more appealing than a random example of such a thing; it is totally plausible that one could find some interesting history on the use of this sieve and slot a paragraph about it into this article or a related one. But, the place you are putting this paragraph is definitely wrong.
It may help you to imagine what would happen in the future were some other editor to come and insist that we include mention of the important and fascinating fact that every prime number is congruent to plus-or-minus 1,2,4,7,8,...,37 mod 75. How should someone explain to this editor (who has a deep and abiding personal belief in the importance of this fact) why it does not belong in the section on distribution of prime numbers? Best, JBL ( talk) 18:47, 26 July 2014 (UTC)
For Quantum connection to zeta function could it be referring to the Casimir Effect? 67.188.92.176 ( talk) 20:05, 10 August 2014 (UTC)Robin Randall, Aug. 2014
"There is no known useful formula that sets apart all of the prime numbers" - is there a useless one? What does "useful" mean? Are there formulas that require computing power beyond our abilities? -- Richardson mcphillips ( talk) 17:52, 6 February 2015 (UTC)
Under "number of prime numbers below a given number" section, you might want to add the derivative of pi(n) n/ln(n) which is [ln(n)-1]/[[ln(n)]^2], which gives the approximate fraction of prime numbers at a certain 'size' number. For example, at the 1,000,000,000 level, you can expect about 46 out of 1000 numbers to be prime. 71.139.161.9 ( talk) 19:37, 7 September 2014 (UTC)
It seems like someone forgot to have a section on the Interval Containing At Least One Prime Number. So, I will suggest it. John W. Nicholson ( talk) 17:55, 1 March 2015 (UTC)
The article claims that the latest prime number was found in April 2014 and later in the sentence links to the wikipedia list of largest prime numbers. However, that article claims that the latest largest prime number was discovered in February 2013. 216.96.200.76 ( talk) 16:13, 14 April 2015 (UTC)
" ...the probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n."
To me this seems to be saying that any two digit number has a 50% chance of being prime, a three digit number has a 1 in 3 chance, etc. Obviously, that's not the case.
Am I just misreading it? — Preceding unsigned comment added by Tym King ( talk • contribs)
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I believe my addition of : "non-prime numbers (or rather, their factorization) can be said to be 'composed' of the primes themselves" has merit, as it makes clear the explanation that immediately follows it. Can we not leave it in? — Preceding unsigned comment added by Baguettes ( talk • contribs) 21:57, 26 September 2015 (UTC)
Again, I am confused when it says pi(11) = 5 for the 5 primes LESS THAN OR EQUAL to 11. Later it appears pi(n) represents the number of primes LESS THAN the number N. Which is it? Or does the approximate operator take care of this? RobinLRandall 15:01, 15 Oct 2015 (UTC) — Preceding unsigned comment added by 67.188.92.176 ( talk)
I just removed a reference to Mathworld regarding the fact that Euler did not consider 1 as a prime number, and replaced it by a direct reference to one of Euler's theorems, from which statement this fact is clear. In fact Weisstein's reference only mentioned that Goldbach considered 1 to be a prime, and not that Euler did not. But this is beside the point. I think we should generally avoid references to Weisstein's online encyclopedy, which is not reliable at all as it contains many approximate and false informations. It has the same disadvantages as Wikipedia has (of having subjects treated by non specialists), with the further drawback of being edited by essentially one single non specialist - Weisstein himself. Sapphorain ( talk) 08:02, 18 November 2015 (UTC)
There has been some recent edit/reversion going on. My feeling is that it would be nice to mention the AKS algorithm (or some other aspect of algorithmics) in the paragraph in question, but that the level of technicality should be kept to the level "could be understood with a high school education." I suggest discussing the text here in order to reach consensus, rather than continuing to edit the article directly. -- JBL ( talk) 22:21, 5 November 2015 (UTC)
The AKS algorithm, which is considered very slow for practical sizes, shows that deciding whether a number n is prime has polynomial complexity, which means that in the general case it can be done quickly. For practical sizes, probabilistic algorithms such as the Miller-Rabin algorithm are preferred, which execute very fast at the cost of some small error probability.
Hi, this is a ridiculously minor thing, but I think the word "surprisingly" should be deleted from the bit about Ulam spirals clustering on certain diagonals, so as to maintain an objective tone. — Preceding unsigned comment added by 140.233.173.75 ( talk) 10:00, 18 December 2015 (UTC)
I'm just a random passer-by, but want to point out that the statement below on the page, about the prime number theorem, is not correct:
... , which says that the probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n.
The prime number theorem defines \pi(x) as the number of primes less than x, and says that is \pi(x) is proportional to log(x).
It says that the probability that a number n chosen at random from [2 ... x] is prime, is proportional to y = log(x).
This is not the same thing as the number of digits of n, the number that was chosen at random. The probability that a random number of exactly n-digits is prime, is proportional to something like \pi(10^n) - \pi(10^n-1). You have to cut out all the numbers that have fewer digits from the pool. — Preceding unsigned comment added by Ccmxxx ( talk • contribs) 16:18, 26 December 2015 (UTC)
My edit has been reverted, restoring the following wording:
True, the m=1 case is just a null product. But the point of my edit was that the old and restored version claims that (m, n)=(1, 0) or (1, 1) gives the number of sides of a constructible regular polygon: a1-sided polygon and a 2-sided polygon respectively. The former is impossible, and the latter is possible only if we admit a degenerate polygon. So I think the wording needs to be corrected. Loraof ( talk) 21:12, 15 March 2016 (UTC)
This article and Euclid's theorem attribute different proofs of the infinitude of primes to Euler. This one says it's about the divergence of the series of prime reciprocals, while the other one involves an Euler product formula for the harmonic series. Are they both Euler's? Shouldn't we be more consistent? — David Eppstein ( talk) 21:48, 17 March 2016 (UTC)
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Number of prime numbers
Prime Numbers Set Definition
Definition of prime numbers can be written all over as this: Prime numbers does not have a factor other than itself and 1; as following;
Sets consists of 's are;
Thus;
P shows prime numbers' set,
Some features of sets are like below,
Set A consists of positive integers starting from 1, set B consists of positive integers greater than 1. Separately multiplying their own members with their own thus getting a new pair of sets. The difference of the new sets is the set of almost prime numbers. 1 is not a member of the prime numbers' set, prime numbers' set could be obtained by substracting 1 from latest found set. If it's desired a N value could be selected by that prime numbers' set can be obtained within the range of 1 to N -- Nexusiot ( talk) 20:46, 2 June 2016 (UTC) Comment : "Please add this new feature" -- Nexusiot ( talk) 20:46, 2 June 2016 (UTC)
Nexusiot ( talk) 20:46, 2 June 2016 (UTC)
All prime numbers have to follow this formula is: 6n±1 — Preceding unsigned comment added by 212.253.111.210 ( talk) 00:33, 5 October 2016 (UTC)
Best regards
Nedim ERDAN — Preceding
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In the list of prime number you have 101 as a prime number, this is incorrect. — Preceding unsigned comment added by Theisencouple ( talk • contribs)
The largest known proth prime in Prime_number#Special-purpose_algorithms_and_the_largest_known_prime is not up-to-date, see also Seventeen or Bust. Due to the protection of the article I can't update it myself. Der Waldkauz ( talk) 12:49, 3 January 2017 (UTC)
I think will be time to give a math definition of primes that match as possible the "talking of" definition:
is a prime if and only if:
This definition respect the known one in the main concept of Prime as result of a recursive division, missing just 2.
From the definition fits for all Naturals.
Usinig this definition and 2 algos involving Sums / Product / Fractions and Integer part of..., it's possible to count the primes and given one find the next one. This algos are of course not computable immediately from very little primes due to factorial product, but in theory they give a perfect definition of Primes as well sorted numbers. So pls delete elsewhere the phrase "we actually don't know if primes are well sorted or not...".
Stefano Maruelli — Preceding unsigned comment added by StefanoMaruelli ( talk • contribs)
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Please add in the References section the information about my new book. [1] Please add in the External links section the link-information about my new book (hope this is correct, because this is my first post ....) <ref prime numbers - new results </ref> Karl-Heinz Kuhl ( talk) 09:33, 22 January 2017 (UTC) Karl-Heinz Kuhl ( talk) 09:33, 22 January 2017 (UTC)
References
article states
It consists of testing whether n is a multiple of any integer between 2 and the square root of n.
for the number 1,999,999 this is not true... the square root of 1,999,999 is 1414.xxx... but the factors of 1,999,999 are 1657, 71, 17... since 1657 is greater than 1414 then 1,999,999 would be considered prime... but it is not... trust this helps I do not know how to sign this Dan Ellwein 2601:3C5:4202:313D:9D48:94A6:1D00:E135 ( talk) 05:34, 8 February 2017 (UTC)Dan Ellwein 2601:3C5:4202:313D:9D48:94A6:1D00:E135 ( talk) 05:34, 8 February 2017 (UTC)— Preceding unsigned comment added by 2601:3C5:4202:313D:9D48:94A6:1D00:E135 ( talk) 05:27, 8 February 2017 (UTC)
Why does the article say that primes are natural numbers? I think this is a serious missinformation. Why are the negative primes not included in presentation?-- 82.79.114.5 ( talk) 08:42, 22 February 2017 (UTC)
My math isn't great and I'm falling asleep, but the prime number article says:
The fundamental theorem of arithmetic article seems to disagree (see the part of this quote I bolded):
I think the prime number article is missing an important part of that sentence. 3 is an integer greater than 1; if 1 is not a prime number, how can 3 be expressed as a product of primes?
So... Yeah. Thank you and good night. 71.121.143.38 ( talk) 08:10, 30 March 2017 (UTC)
I found a great article from the Institute for Advanced Study that I thought might could contribute some to the prime number article!
https://www.ias.edu/ideas/2013/primes-random-matrices — Preceding unsigned comment added by 2001:4642:11C6:0:5D:4668:A89:EB74 ( talk) 18:28, 1 July 2017 (UTC)
For a long time, when all the prime numbers up-to some given number were evaluated, it was expected that its 'distribution'/'count off' must/can be represented by a simple analytical function. The distribution of prime numbers is indeed be a pattern related phenomenon but the means that pattern has been sought is misguided/ill-advised, according to Yoldas Askan, a British scientist and mathematician. In his paper, Yoldas challenges some of the fundamental understanding of Prime Numbers and reconsiders these definitions, and ultimately arrives at his analytical formula. In his view, there is no great deal about functions that are approximations because there can be infinitely many of these derived but only suitable at certain number interval. Yoldas claims that the 'beautiful' thing about the Prime number distribution is that there will be no analytical function [of any complexity] that will compute and provide exact values for π(x) other than the Prime Number Distribution Series, which is provided as follows, — Preceding unsigned comment added by Nuclearstrategy7 ( talk • contribs) 17:37, 14 July 2017 (UTC)
This has languished on the ArXiv for very long without actually being published – presumably because it is apparently so long that Helfgott's website lists it as to appear as a standalone book. Mind you, if it had not already long since been checked and accepted, one wonders why he got the Humboldt professorship specifically for it. Double sharp ( talk) 13:23, 17 July 2017 (UTC)
I have requested comments at Wikipedia talk:WikiProject Mathematics. Double sharp ( talk) 14:01, 17 July 2017 (UTC)
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There is a new theory is called ASA method, gives a solution to the prime numbers in generation and distribution, Read the published Paper -- Alsumery2 ( talk) 22:24, 2 September 2017 (UTC)
The discussion has become meaningless and sterile Some users are not specialists who are not worthy of the subject-matter evaluations, leaving the subject and going beyond the core of the research is unfortunate Alsumery2 ( talk) 15:28, 3 September 2017 (UTC)
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In the "Special-purpose algorithms and the largest known prime" section, it says:
For example, the Lucas' primality test requires the knowledge of the prime factors of n − 1, while the Lucas–Lehmer primality test needs the prime factors of n + 1.
I believe the second link is a typo and should point to some other page. The article for the Lucas-Lehmer test does not suggest that it needs the prime factors of n + 1. Unfortunately, I don't know which article link should be put in its place. The article for the Lucas test does not provide a mention of its n + 1 counterpart. Additionally the MersenneWiki page on primality tests lists only one test that needs the factors of n + 1, calling it "Morrison's Theorem," but the link is dead and I can't find a reference to this theorem online. Derek M ( talk) 23:01, 7 January 2018 (UTC)