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I found out another published work done by Mr. A.Venugopalan aka Atiyolil Venugopalan on Prime numbers. The paper was published in the Hardy-Ramanujan Journal Vol.6 (1983) 45-48.
It could be viewed at the link:
https://hrj.episciences.org/99 — Preceding
unsigned comment added by
70.192.21.85 (
talk) 14:47, 10 August 2014 (UTC)
The following four formulas were published in the Proceedings of the Indian Academy of Sciences. Volume 92, No.1 September 1983 edition, pages 49-52.
Formula for (n+1)th Prime
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---|
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Formula for the Twin primes
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For P differs from zero, P is the first Twin prime between and and it is given by the formula below:
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Formula for number of Primes
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---|
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Formula for number of Twin-primes
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What is MathSciNet? Please look at the Proceedings of the Indian Academy of Sciences. Volume 92, No.1 September 1983 edition, pages 49-52. — Preceding unsigned comment added by 64.121.225.161 ( talk) 00:40, 16 August 2014 (UTC)
The importance of Mr. Venugopalan's formulas for prime numbers is that he is the first person who discovered explicit formulas for prime numbers, especially, for twin prime numbers and number of twin primes(emphasis added)! It is very surprising to note that to this day, no proof has been found to show there exists infinite number of twin primes even though Mr. Venugopalan brought us to the verge of showing whether or not there are infinite twin primes with his explicit formulas in 1983. — Preceding unsigned comment added by 24.173.7.42 ( talk) 18:32, 6 January 2019 (UTC)
The recurrence does generate all the primes, but this is entirely dependent on being an encoding of the sequence of primes. Unlike with other formulas on the page, this formula has little to do with prime numbers. In fact, many sequences can be generated with this formula with the right choice of . For example, using will generate the sequence , and using
will generate the sequence . If this section is not removed, I think the section should at least note that many arbitrary sequences can be generated with this formula. Rzvhkon ( talk) 03:18, 30 November 2020 (UTC)
A discussion is taking place to address the redirect 2.9200.... The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 September 14#2.9200... until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Ivanvector's squirrel ( trees/ nuts) 16:40, 14 September 2021 (UTC)
Some different IPs have recently been trying to add the text
to the article. This formula does not produce only prime numbers. When is a composite pseudoprime for the base 2 (the numbers 341 = 11 x 31, 561 = 3 x 187, 645 = 3 x 5 x 43, 1105 = 5 × 13 × 17, etc as listed in OEIS:A001567) it will be produced by this formula, even though it is a composite number. If additional attempts at adding this material are made, they should be reverted on sight. — David Eppstein ( talk) 06:54, 11 January 2022 (UTC)
The section § Possible formula using a recurrence relation gives the formula for Rowland's prime-generating sequence, with the first term a1 set to 7, the first differences of which give "1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, ..." (sequence A132199 in the OEIS). It then goes on to explain that this sequence will not produce 2.
However, via the OEIS page for A132199 I came upon A134734, which is the same idea but with a1 set to 4. It is observed that this sequence is identical to A132199 (a1=7), except for the first two terms: A134734 (a1=4) starts with "2, 3, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, ...". The base sequence ( A084662, "4, 6, 9, 10, 15, 18, ...") from which the differences are calculated is identical to the base sequence of the a1=7 case ("7, 8, 9, 10, 15, 18, ...") after the first two indices, and there's no offset in the subscript n (a3=9 in both, etc).
So, is there a particular reason why this article explains the a1=7 case and its lack of 2, instead of the a1=4 case, which starts with 2? I can see merits for both cases, I'm just curious whether there's a reason for this. oatco (talk) 21:35, 22 May 2022 (UTC)
I suggest to state that the solution is in non-negative integers rather than in natural numbers, as M. says in his article (also because the link gives TWO different definitions of natural numbers).
I suppose that no solutions are known; if true I would feel more relaxed (excuse my poor english) in reading this explicitly.
The text says that the set may be in 9 variables, then says that the polynomial is in 10 variables. Surely it is right because refer to different items, but it is possible to be more explicit on these two items?
Thanks. Pietro. 151.29.150.78 ( talk) 15:25, 16 January 2023 (UTC)
The article lead says no formula for computing primes is known which is efficiently computable. What does "efficiently computable" mean in this context? The linked article lists a bunch of asymptotic classes, but it doesn't say which classes count as "efficiently computable". Does it mean not formula computable in polynomial time? - lethe talk + contribs 18:39, 9 May 2023 (UTC)
Plouffe's formulas are conjectural and have not been proven. Does this section really belong here? MathPerson ( talk) 16:59, 19 July 2023 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 10 sections are present. |
I found out another published work done by Mr. A.Venugopalan aka Atiyolil Venugopalan on Prime numbers. The paper was published in the Hardy-Ramanujan Journal Vol.6 (1983) 45-48.
It could be viewed at the link:
https://hrj.episciences.org/99 — Preceding
unsigned comment added by
70.192.21.85 (
talk) 14:47, 10 August 2014 (UTC)
The following four formulas were published in the Proceedings of the Indian Academy of Sciences. Volume 92, No.1 September 1983 edition, pages 49-52.
Formula for (n+1)th Prime
|
---|
|
Formula for the Twin primes
|
---|
For P differs from zero, P is the first Twin prime between and and it is given by the formula below:
|
Formula for number of Primes
|
---|
|
Formula for number of Twin-primes
|
---|
|
What is MathSciNet? Please look at the Proceedings of the Indian Academy of Sciences. Volume 92, No.1 September 1983 edition, pages 49-52. — Preceding unsigned comment added by 64.121.225.161 ( talk) 00:40, 16 August 2014 (UTC)
The importance of Mr. Venugopalan's formulas for prime numbers is that he is the first person who discovered explicit formulas for prime numbers, especially, for twin prime numbers and number of twin primes(emphasis added)! It is very surprising to note that to this day, no proof has been found to show there exists infinite number of twin primes even though Mr. Venugopalan brought us to the verge of showing whether or not there are infinite twin primes with his explicit formulas in 1983. — Preceding unsigned comment added by 24.173.7.42 ( talk) 18:32, 6 January 2019 (UTC)
The recurrence does generate all the primes, but this is entirely dependent on being an encoding of the sequence of primes. Unlike with other formulas on the page, this formula has little to do with prime numbers. In fact, many sequences can be generated with this formula with the right choice of . For example, using will generate the sequence , and using
will generate the sequence . If this section is not removed, I think the section should at least note that many arbitrary sequences can be generated with this formula. Rzvhkon ( talk) 03:18, 30 November 2020 (UTC)
A discussion is taking place to address the redirect 2.9200.... The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 September 14#2.9200... until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Ivanvector's squirrel ( trees/ nuts) 16:40, 14 September 2021 (UTC)
Some different IPs have recently been trying to add the text
to the article. This formula does not produce only prime numbers. When is a composite pseudoprime for the base 2 (the numbers 341 = 11 x 31, 561 = 3 x 187, 645 = 3 x 5 x 43, 1105 = 5 × 13 × 17, etc as listed in OEIS:A001567) it will be produced by this formula, even though it is a composite number. If additional attempts at adding this material are made, they should be reverted on sight. — David Eppstein ( talk) 06:54, 11 January 2022 (UTC)
The section § Possible formula using a recurrence relation gives the formula for Rowland's prime-generating sequence, with the first term a1 set to 7, the first differences of which give "1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, ..." (sequence A132199 in the OEIS). It then goes on to explain that this sequence will not produce 2.
However, via the OEIS page for A132199 I came upon A134734, which is the same idea but with a1 set to 4. It is observed that this sequence is identical to A132199 (a1=7), except for the first two terms: A134734 (a1=4) starts with "2, 3, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, ...". The base sequence ( A084662, "4, 6, 9, 10, 15, 18, ...") from which the differences are calculated is identical to the base sequence of the a1=7 case ("7, 8, 9, 10, 15, 18, ...") after the first two indices, and there's no offset in the subscript n (a3=9 in both, etc).
So, is there a particular reason why this article explains the a1=7 case and its lack of 2, instead of the a1=4 case, which starts with 2? I can see merits for both cases, I'm just curious whether there's a reason for this. oatco (talk) 21:35, 22 May 2022 (UTC)
I suggest to state that the solution is in non-negative integers rather than in natural numbers, as M. says in his article (also because the link gives TWO different definitions of natural numbers).
I suppose that no solutions are known; if true I would feel more relaxed (excuse my poor english) in reading this explicitly.
The text says that the set may be in 9 variables, then says that the polynomial is in 10 variables. Surely it is right because refer to different items, but it is possible to be more explicit on these two items?
Thanks. Pietro. 151.29.150.78 ( talk) 15:25, 16 January 2023 (UTC)
The article lead says no formula for computing primes is known which is efficiently computable. What does "efficiently computable" mean in this context? The linked article lists a bunch of asymptotic classes, but it doesn't say which classes count as "efficiently computable". Does it mean not formula computable in polynomial time? - lethe talk + contribs 18:39, 9 May 2023 (UTC)
Plouffe's formulas are conjectural and have not been proven. Does this section really belong here? MathPerson ( talk) 16:59, 19 July 2023 (UTC)