# Talk:Mersenne prime

Active discussions
WikiProject Mathematics (Rated C-class, Mid-priority)

## Mersennes in nature and pernicious

I removed the following text from the introduction:

equivalently that they be pernicious Mersenne numbers, namely those numbers whose binary representation contains a prime number of ones and no zeros

and this from "Mersenne numbers in nature":

In computer science, unsigned n-bit integers can be used to express numbers up to Mn. Signed (n + 1)-bit integers can express values between −(Mn + 1) and Mn, using the two's complement representation.

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)

## Incomprehensible paragraphs

The section about "primitive part" is impossible to understand to the largest part of it. For example,

Besides, if we notice those prime factors, and delete "old prime factors", for example, 3 divides the 2nd, 6th, 18th, 54th, 162nd, ... terms of this sequence, we only allow the 2nd term divided by 3, if we do, they are ...

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)

@MFH: I agree and have removed the section. Which other section(s) have the same problem, in your estimation? --JBL (talk) 18:26, 5 December 2018 (UTC)
Incidentally, the section is at least 3 years old (I got bored of looking back further). --JBL (talk) 18:33, 5 December 2018 (UTC)

## Mersenne numbers in nature and elsewhere

Hi, currently reads that the wheat and chessboard issue is solved by M64, which is not the case. It's solved by T64, which is not the same thing. This needs to be correctly rectified. Beast01998 (talk) 12:29, 15 February 2020 (UTC)

I don't think we'll even know what M64 is for another 20 or so years; the sequence is only known to M51 (I'm expecting M52 to have an exponent around 120 million; after that I don't consider it appropriate to talk about prematurely because we should only think one exponent into the future, meaning we must wait until 63 Mersenne primes are known before we can talk about M64.) Georgia guy (talk) 12:34, 15 February 2020 (UTC)
It's well-settled that ${\displaystyle M_{64}}$  denotes the 64th Mersenne number, not the 64th Mersenne prime.--Jasper Deng (talk) 12:37, 15 February 2020 (UTC)
I guess you read Wheat and chessboard problem#Solutions. That section defines ${\displaystyle T_{64}}$  as the total number of grains on 64 squares, and then calculates the value which is ${\displaystyle M_{64}}$  in our Mersenne number notation defined in the lead. The letter T was probably chosen as the first letter of total. I have seen M64 as notation for the 64th Mersenne prime (actually smaller numbers like M45 for the 45th) but not ${\displaystyle M_{64}}$ . Our article says the solution is ${\displaystyle M_{64}}$  so we have no problem. PrimeHunter (talk) 13:42, 15 February 2020 (UTC)

Ok, not really. But: the infobox asserts a "publication year" of 1536, in a publication by Hudalricus Regius. There is a "reference" but actually it just a link to a google book version of what is apparently the Regius publication. None of this is mentioned in the history section of the article. So: the most prominently placed date and author information in the article is completely unsupported by sources and article text. This is ... not a good situation. (Pinging whose edits brought this to my attention.) --JBL (talk) 18:16, 24 March 2020 (UTC)

It was also discussed at Talk:Mersenne prime/Archive 1#Infobox Confusion with no action. https://primes.utm.edu/mersenne/#hist says Regius showed 211−1 is composite. Later it claims he also made a false list of alleged primes but after the first mention it says Cataldi made a false list. Maybe the author confused the two. Regardless, Regius does not belong in the infobox when the form of primes was already discussed by Euclid. I have removed him.[1] He may be mentioned in the history section. PrimeHunter (talk) 18:45, 24 March 2020 (UTC)
Thanks (and thanks for pointing to the earlier discussion). A good secondary source on the pre-Mersenne history would be wonderful. --JBL (talk) 21:34, 24 March 2020 (UTC)

## Cole's talk

If he didn't speak, is it still a talk? Double sharp (talk) 04:23, 15 March 2021 (UTC)

Hmm. It seems quite plausible that the common account may have been a fictional dramatisation by E. T. Bell. Double sharp (talk) 07:51, 16 March 2021 (UTC)

## 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, Mp 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 (talkcontribs)

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

## List of known Mersenne primes

, :, :, :@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)
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)