Talk:Largest known prime number

M₁₃ a.k.a, 8191

In the history section, the first number of the list, under Discoverer lists ˝Anonymous˝ but fr:8 191 cites Abû Tahir Ismail al-Mardini as the discoverer. Should this change— Preceding unsigned comment added by Pqnlrn (talk • contribs) 15:46, 25 July 2019 (UTC)

6700417

Well, it seems Euler never actually said in print that it was prime; however, he had already done over half the work to prove it so, and apparently some experts believe he knew it anyway for the reason that the remaining work would not have taken him very long (it amounts to six trial divisions). (But then, why didn't he include it in the table of large primes he prepared in 1762?) So I have added a disclaimer about this. Double sharp (talk) 10:33, 18 April 2020 (UTC)

Moore's law

The chart showing increase in number of digits suggests that Moore's law is at work here. The connection is noted in Introduction to Cryptography]. SpinningSpark 17:19, 19 June 2020 (UTC)

Incorrect decimal expansion for 180×(M₁₂₇)²+1

I noticed that the decimal expansion entry for the prime number with the notation 180×(M₁₂₇)²+1 is currently:
5210644015679228794060694325390955853397149309953825381775591280356090833797121
From what I can tell, this number is neither prime nor what the notation should expand to.

The correct number should be:
5210644015679228794060694325390955853335898483908056458352183851018372555735221

Could someone double check this before editing the page? Aerdil (talk) 07:13, 27 June 2020 (UTC)

@Aerdil: Well spotted. I have fixed it.[1] Thanks. The wrong number was added by Putian Ye in [2]. It falsely computed M₁₂₇ as 2¹²⁷ instead of 2¹²⁷-1. I have checked all other numbers added in the edit and they are correct. PrimeHunter (talk) 08:02, 27 June 2020 (UTC)

​​​​ I have spotted this non-prime at d:Q90570083 (then here). Fixed. Regards, —Mykhal (talk) 21:53, 31 December 2021 (UTC)

But Is There a Largest Prime Number in Theory?

I came to this article because I wanted to know the answer to the question: is there a proof that a largest prime number does or does not exist. I don't see that question addressed at all. I think it should be included in the article, is there a proof one way or another or is it an open question? --MadScientistX11 (talk) 04:30, 12 February 2021 (UTC)

I think the answer to my question is that Euclid proved there is no largest prime: Euclid prime proof. I think it would be a good idea to add that to the article. --MadScientistX11 (talk) 04:32, 12 February 2021 (UTC)

It's already in the second paragraph of the lead. PrimeHunter (talk) 22:05, 23 April 2021 (UTC)

Largest Probable Prime

The 5794777-repdigit 11111111...11111111 found Apr 20, 2021 by Ryan Propper & Sergey Batalov deserves to listed, but with a pointer to the Probable Prime page. EdPeggJr (talk) 04:30, 23 April 2021 (UTC)

Wikipedia:Articles for deletion/Titanic prime and the large prime number article proposal

D.Lazard has a proposal to bring together coverage of the search for large prime numbers under one article, large prime number, and has suggested that this article might provide the best starting point from which to build that article. I think it might be beneficial if (i) more editors weighed in at the AfD and (ii) we talked in more detail about how all of this material might best be organised. — Charles Stewart (talk) 08:41, 14 May 2021 (UTC)

I agree, Titanic primes should be de-listed since it overemphasizes the Lucas-Lehmer test. The new page should list largest primes proven by different primality tests. I recently added the largest probable prime R8177207 to this page with the distinction that it's not proven. 98.226.112.251 (talk) 14:57, 14 May 2021 (UTC)

This page semms like part of a large prime number, so it seems like we can already move this page to a large prime number. That may make the merge discussion easier.--SilverMatsu (talk) 05:28, 15 May 2021 (UTC)

Numbers of digits in this prime number

The power of 2 is 82589933 so By math,we can say n=8258993 The number of digit = 3n+1

                                   = 3×8258993 + 1
                                   = 24776979 + 1
                                   = 24776970 digits 

So, 24776979 exactly digits in this prime number This is wrong that the numbers of digits in this prime number is 24862048.

If you want to any thing about this then reply. Thank you 2402:3A80:1F8C:9BC5:0:0:6C0:35A1 (talk) 18:40, 17 November 2021 (UTC)

You have several errors, starting with omitting an ending "3" in 82589933. The correct formula is ceil(n × log₁₀(2)) = ceil(82589933 × 0.3010299956...) = 24862048. The article is right. PrimeHunter (talk) 19:04, 17 November 2021 (UTC)

Definition of "known"

This article doesn't have any explanation of what it means for a prime number to be classified as "known". I think this should be fixed. Mexicochina (talk) 03:37, 23 December 2023 (UTC)

When the meaning of "known" primes is discussed at all in sources, it's about what constitutes a valid primality proof. Your edits show your concern is what it means for the actual number to be "known" when you have some formula or description of the number. That's a complete non-issue in sources so we shouldn't make it an issue. Quoting from my edit summaries: Reliable sources agree which primes are known without formally defining it. Wikipedia is based on sources and shouldn't invent a definition. Sources apparently haven't found a need to formalize it but everybody agrees that a decimal/binary expansion or simple formula like 2^p-1 is a known prime while a prime search algorithm expressed as a formula with a humongous number of steps is not a known prime. With currently known primality proving methods there is no gray zone between such clear cases so we have no good reason to make it sound problematic. Our main reliable source is titled Largest Known Primes. I have a website http://primerecords.dk and have personally found numerous prime records during many years and have participated in discussions with other record setters at many websites. When reliable sources agree what the largest known primes are, we can just list the primes with sources and should not attempt to make our own definition based on original research. PrimeHunter (talk) 12:34, 23 December 2023 (UTC)

I'm not trying to impose any definition of "known" of my own, I'm just pointing out that the article lacks any definition of this word. If you think that is what "known" should mean, please include it in the article. We can't just include a word with a fuzzy definition in the title and just expect the reader to guess what it means. Especially when this is an article about mathematics.

There are methods of writing "the n-th prime number" with mathematical notation where n could be any number and these should obviously be excluded from the article, but at least the article should make it clear why and how these kind of constructions were excluded. Mexicochina (talk) 21:26, 23 December 2023 (UTC)

It is rather clear that, for the sources and in this context, "known prime number" means "number that is known to be prime" and not "prime number that is known". Many numbers are known to be probably prime, but are not "known prime numbers" because no primality proof has ever been provided. D.Lazard (talk) 14:13, 23 December 2023 (UTC)