Talk:Formula for primes

message: The recurrence 
f_n = \left\lfloor f_{n-1} \right\rfloor
(f_{n-1} - \left\lfloor f_{n-1} \right\rfloor + 1 )
 does generate all the primes, but this is entirely dependent on f_1 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 p_n can be generated with this formula with the right choice of f_1. For example, using
f_1 = e = 2.71828182845\ldots 
will generate the sequence p_n=n+1, and using
:f_1 = \sum_{n=1}^{\infty} \left((n+2)^2 - 1\right) \left(\prod_{i=1}^{n-1} (i+2)^2 \right)^{-1} = 9.84343604644290\ldots 
will generate the sequence p_n=(n+2)^2. 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)
thread_title:  Is the section "A function that represents all primes" relevant? 

message: 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)
thread_title:  "2.9200..." listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Some different IPs have recently been trying to add the text
:Another similar formula is f(n) = \left\lfloor \frac{(2^n-2) \bmod (n+1)}{n} \right\rfloor (n-1) + 2
to the article. This formula does not produce only prime numbers. When n+1 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)
replies: text: I don't know, who posted "false" formula, but... thank you for your comment/discussion, David. Calculation of (2^n-2) is faster than (n!). After getting pseudoprime numbers f_n = f(n) you can make Primality test: slow Wilson's theorem f_{n-1}!\ \equiv\; -1 \pmod{f_n}, slow Trial division or fast APR-CL (Adleman–Pomerance–Rumely + Cohen–Lenstra). Mvitaminus (talk) 08:42, 24 November 2022 (UTC)
thread_title:  False formula 

message: The section  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, ..." . It then goes on to explain that this sequence will not produce 2.
However, via the OEIS page for A132199 I came upon , 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 (, "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)
replies: text:  there are superior algorithms akin to Rowland's, at least in terms of distinct primes found in X evaluated terms, as well as computing speed.  Several are at the OEIS, A135508 is one, another was just published by Bouras https://easychair.org/publications/preprint/k83H Billymac00 (talk) 00:20, 27 August 2022 (UTC)
thread_title:  Rowland's prime-generating recurrence relation 

message: 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)
replies: text: . This seems pretty obvious, since the nonnegative integers are referred to later in the section. Thank you for pointing this out.—Anita5192 (talk) 17:08, 16 January 2023 (UTC)
thread_title:  comments on diophantine equations 

message: 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)
thread_title:  what does efficiently computable mean in this context? 

message: Plouffe's formulas are conjectural and have not been proven. Does this section really belong here? MathPerson (talk) 16:59, 19 July 2023 (UTC)
replies: text: Since no practical formula has been found and this section is sourced, I think it should stay.—Anita5192 (talk) 17:10, 19 July 2023 (UTC)
thread_title:  Plouffe's formulas