Talk:Mersenne prime

Factorization of composite Mersenne numbers

This section says, "However, not all Mersenne numbers are Mersenne primes, and the composite Mersenne numbers may be factored non-trivially."

I don't know exactly what this last clause means. Is is merely saying that there are factorizations other than N times 1? Or that it takes non-trivial effort to factor these N? Moreover, for large primes p, M_p usually can NOT be factored with current computers and algorithms.

Therefore, I would recommend just deleting the last clause so it reads, "However, not all Mersenne numbers are prime." MathPerson (talk) 17:34, 25 June 2021 (UTC)

Not all Mersenne numbers are prime?? That's easy to prove. There are numbers of the form 2^n-1 that are divisible by p for all odd primes p. Georgia guy (talk) 17:41, 25 June 2021 (UTC)

Prime factorization of 2^43-1

I'm 431x9719x2099863, the prime factorization of 2⁴³ - 1. 431x9719x2099863 (talk) 14:54, 18 August 2021 (UTC)

I had replaced the row 2⁴³ - 1 with my signature for the prime factorization. 431x9719x2099863 (talk) 14:55, 18 August 2021 (UTC)

The account of 431x9719x2099863 (talk | contribs) is now globally locked. — Anita5192 (talk) 16:14, 18 August 2021 (UTC)

Larger Mersenne primes

I think there are such Mersenne primes above the largest known Mersenne prime (at tetrational level, such as a prime number above 2 ↑↑ 10), so it is conjectured that there are infinitely many Mersenne primes. 2405:9800:BA31:F6:FD7E:6343:96DA:9CBD (talk) 05:31, 4 September 2021 (UTC)

Yes, Mersenne prime#About Mersenne primes says it is conjectured. PrimeHunter (talk) 14:32, 6 September 2021 (UTC)

Composite Number error

In the opening paragraph, how is the following sentence correct?

If n is a composite number then so is 2ⁿ − 1.

If n is 4, a composite number, then 2⁴ − 1 which is 15, is not composite. — Preceding unsigned comment added by Sstair (talk • contribs)

15 = 3 × 5, which is composite.—Anita5192 (talk) 14:00, 6 September 2021 (UTC)

List of known Mersenne primes

@GorillaWarfare:, :@Fowler&fowler:, :@JayBeeEll:, :@Eviolite: I disagree with moving the table of known Mersenne primes to a new article. I think the table should stay in the Mersenne prime article, because it is easier to read information in one location instead of jumping back and forth. Best regards Szelma W (talk) 13:50, 14 October 2021 (UTC)

@Szelma W: I did not find the article particularly readable with large amounts of text separated by a large table taking up the entire screen (this is still somewhat of an issue currently with lots of existing unsourced tables and such). If a reader is just interested in learning about Mersenne primes, I don't think it's very helpful to tell them all 51 entries with lots of info on each unless they specifically seek it out. The indices are still present in that sections, just in text form, and stuff like major discoverers is repeated in the "searching for Mersenne primes" section above. Thanks, eviolite (talk) 15:15, 14 October 2021 (UTC)

@Eviolite: Hello! I prefer to keep information about the same subject in one location. I think the Mersenne prime article was clear enouth in the previous format. Nobody complained about the format of the article until now, when Wikipedia tries to build a set of diffrent kind of lists. I think the table with known Mersenne primes should stay in the article. I agree that the table should be simplified. The large Mersenne primes could be exchanged with links to Internet sites which keep the values in text files. Regards Szelma W (talk) 21:10, 14 October 2021 (UTC)

@Szelma W: Please see Wikipedia's policy on external links. Particularly, With rare exceptions, external links should not be used in the body of an article and WP:ELLIST which states lists themselves should not be composed of external links. It is against policy to do as you suggest and link to external files with full numbers. Beyond that suggestion I see nothing vital to include in this article that isn't already there (the indices are there, and the first few reasonably-long Mersenne primes are in the lede). --eviolite (talk) 23:19, 14 October 2021 (UTC)

@GorillaWarfare: Hello! What is your opinion about the above? Szelma W (talk) 21:10, 14 October 2021 (UTC)

I have no opinion. As far as I know I've never worked on this article. GorillaWarfare (she/her • talk) 02:46, 15 October 2021 (UTC)

I think the list / article separation is an improvement: the separation makes navigation of this article (for people who are looking for facts about Mersenne primes) much easier, and people who for whatever reason want the list should have no difficulty following one link in the clearly labeled section. (And of course this article is also clearly linked in the list.) --JBL (talk) 12:11, 15 October 2021 (UTC)

Incidentally, there was a discussion of this split in advance, just in a slightly unusual place: see Wikipedia_talk:WikiProject_Mathematics#List_of_perfect_numbers_and_Mersenne_prime#List_of_known_Mersenne_primes. --JBL (talk) 12:12, 15 October 2021 (UTC)

Infinite Number of Mersenne Primes

Why is "Are there infinitely many Mersenne primes?" listed as unsolved? Isn't it proven already? https://journalspress.com/LJRS_Volume20/972_There-are-Infinitely-Many-Mersenne-Primes.pdf 2604:3D08:D177:B500:ACD5:551B:6D2B:D195 (talk) 17:27, 17 October 2022 (UTC)

No, that's a crank publication in a predatory journal. --JBL (talk) 18:44, 17 October 2022 (UTC)

All Mersenne numbers with the prime exponents not only primes pass the Fermat primality test for a = 2.

The part of the article starting with the following sentence

"All Mersenne numbers with the prime exponents not only primes pass the Fermat primality test for a = 2"

is own work of Mr. Matt Kalinski (possibly the Wikipedia user with the Mattedia nick). It is not confirmed by any other RS.

Is it allowed to add this kind of edits to the Wikipedia?

Regards Szelma W (talk) 11:01, 24 September 2023 (UTC)

Incorrect Statements in the Theorems about Mersenne numbers section since Dec 7 2013?

In the Theorems about Mersenne numbers section of the Mersenne Prime page I believe there is incorrect information. The statements I am referring to are part of the 3rd bullet point the discusses the form for factors of Mersenne numbers. (I am not saying the main point of this section is wrong, just there is an incorrect statement made.) Specifically, the sentence I believe to be incorrect is:

"As a result, for all positive integers x, q is a factor of 2^x − 1 if and only if p is a factor of x."

If I understand the statement correctly, then counter-examples are easy & plentiful. For example, a counter-example would be:

Let x = 5*7 = 35. (So the only factors of x are 5 and 7.)

Then q = 71 is a factor of 2^x − 1. (2³⁵ − 1 = 0 mod 71)

So for the "if and only if" statement to be correct, then q (or 71) needs to be a factor of 2⁵ − 1 or 2⁷ − 1, but neither of those are true. Indeed, you can easily check all smaller x, and find that the smallest x where q=71 is a factor of 2^x − 1 is x=35.

I checked the edit history and see that this information has been a part of the article since Dec 7, 2013 -- added by @User:Blackbombchu. So I am surprised it could be incorrect and exist on the page for so long. (Which makes me question if I am correct about calling this information incorrect, but it certainly seems incorrect to me.)

(I am not sure if this is the appropriate place to make this report of incorrect information, if there is a more appropriate way to report this suspected mistake please let me know.) Ssebeny (talk) 20:56, 16 September 2024 (UTC)

What is p supposed to be in your example? (Whether or not you're right, it is certainly a problem that the section in question consists entirely of OR by the various people who wrote it, with no reliable sources.) --JBL (talk) 01:04, 17 September 2024 (UTC)

For the counter-example I provide, x=35 so the only factors of x are 5 & 7. You could take p=5 & c=7, or p=7 & c=5. Either way, q=71 is not a factor of 2⁵ − 1 or 2⁷ − 1 and is a factor of 2³⁵ − 1, which seems to violate the if and only if portion of the statement in the article at a minimum. Ssebeny (talk) 03:35, 17 September 2024 (UTC)

Hi! I do not understand your doubts. The first sentence of the theorem says: "If p is an odd prime, then every prime q that divides 2^p − 1"

In your example q=71 is not a divisor of 2^p − 1 either for p=5 or p=7

The sentence "As a result, for all positive integers x, q is a factor of 2^x − 1 if and only if p is a factor of x." is also correct as given in your example q=71 is the factor of 2^x − 1 for x=35 and p=5 or p=7 are factors of x=35. Regards

Szelma W (talk) 12:40, 17 September 2024 (UTC)

Section "Recent development" is irrelevant (and self-promotional)

This section is identical to what the same user keeps inserting into https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test - and in both cases this material is irrelevant (and self-promotional). Suggest prompt removal as well as a serious editorial/admin discussion with that user. Serge Batalov (talk) 21:11, 16 October 2024 (UTC)

When I explain that the material is irrelevant, the user resorts to blames of discrimination as well as my incompetence. And both are untrue - I am discussing strictly the text meterial of the section and its suitability for both Wiki articles. Serge Batalov (talk) 21:16, 16 October 2024 (UTC)

Reference 40 seems irrelevant.

40. Zalnezhad et al. leads to a vacuous unpublished preprint that has no connection to the subject. Suggest removal. Serge Batalov (talk) 06:58, 22 October 2024 (UTC)

I agree and have removed it. --JBL (talk) 23:56, 22 October 2024 (UTC)