Talk:Megaprime

Titanic prime was nominated for deletion. The discussion was closed on 20 May 2021 with a consensus to merge. Its contents were merged into Megaprime. The original page is now a redirect to this page. For the contribution history and old versions of the redirected article, please see its history; for its talk page, see here.

Bevaprime?[edit]

It says that Bevaprime has been suggested as a name for a prime that contains at least 1 thousand million digits. However, as a Megaprime contains at least 1 million digits, surely the logical extension to 1 thousand million digits would be a Gigaprime? 79.77.203.214 (talk) 21:04, 13 March 2010 (UTC)[reply]

You must contact Chris Caldwell if you want to know why he suggested this name. Georgia guy (talk) 21:16, 13 March 2010 (UTC)[reply]

Bevaprime problem[edit]

We know that the smallest 1,000,000,000-digit number is 10^999,999,999. (For short, we'll call this number Beva.) We know it is not prime because it is even. Beva plus 1 is divisible by 11 and obviously not prime. Beva plus 2 is even. Question: Does Beva plus 3 have any known factors?? Georgia guy (talk) 13:43, 14 June 2012 (UTC)[reply]

I am not aware of any factors, but according to the prime number theorem the chance that Beva plus 3 is prime is 1 / (ln(Beva+3)), so it seems extremely unlikely. This site lists factorizations of small numbers of the form 10ⁿ+3 and is the only source I found investigating those numbers. -- Toshio Yamaguchi 00:43, 6 January 2013 (UTC)[reply]

It takes a small fraction of a second to find the prime factor 23. There are no other factors below 10⁸. In PARI/GP (not the fastest option but flexible and easy to use):

? forprime(p=2,10^8,if(Mod(10,p)^999999999+3==0,print(p)))
23
?

PrimeHunter (talk) 03:53, 6 January 2013 (UTC)[reply]

That clearly proves it's composite. How about Beva plus 7?? Georgia guy (talk) 12:41, 6 January 2013 (UTC)[reply]

I don't think the chances of finding a prime of that size by mere trial and error are very good. The prime number theorem suggests to me that most numbers in a range of that size will be composite, so for a good chance to actually find a prime you would have to test a lot of candidates. (Note that you could already eliminate a lot of non-candidates by trial division with some small factors, I think most projects searching for large primes do a preliminary sieving to eliminate such non-candidates). However, I guess storing the sieved list for numbers of such size would require a lot of memory, so I don't know whether that would be possible (or practical) with the memory available on modern computers. -- Toshio Yamaguchi 21:58, 6 January 2013 (UTC)[reply]

? forprime(p=2,10^8,if(Mod(10,p)^999999999+7==0,print(p)))
647
?

Let's stop the search here. If no small factor is found then it would take decades or centuries to make a probable prime test which would be more than 99.99999% likely to say composite, and if it didn't then it would still be impossible to prove primality for that form with any known method. PrimeHunter (talk) 01:04, 7 January 2013 (UTC)[reply]

Does this page only list primes or also PRPs?[edit]

Is the scope of this page only numbers where primality has been proven or also PRPs? If the latter, then it might be worth mentioning 10⁹⁹⁹⁹⁹⁹ + 593499. -- Toshio Yamaguchi 13:53, 1 March 2013 (UTC)[reply]

I added a table containing all known megaprimes and mega PRPs. It is not complete yet. I will add the missing entries as time permits it. -- Toshio Yamaguchi 08:08, 8 April 2013 (UTC)[reply]

File:Megaprime found.png[edit]

I don't understand what this graphic is showing. What do the x and y values stand for? For example, what does the number 9 on the x-axis denote? The y-axis seems to be the number of megaprimes found in a particular year, although the numbers don't seem to be correct. For example, if 12 means 4 megaprimes have been found in 2012, then this seems to be incorrect, because according to http://primes.utm.edu/primes/lists/all.txt, which the graphic seems to be based on, 18 megaprimes were discovered in 2012. -- Toshio Yamaguchi 09:12, 8 April 2013 (UTC)[reply]

It appears to me that to get the year of discovery, one must add 1998 to the number on the x-axis of the graph. Thus 1 stands for 1999; 2 for 2000; 3 for 2001; etc.. JRSpriggs (talk) 08:08, 20 June 2013 (UTC)[reply]

Thanks for clearing that up. I expanded the image description for clarification in the article. -- Toshio Yamaguchi 08:28, 20 June 2013 (UTC)[reply]

Phi[edit]

I note that a dozen of the entries in the table are expressed in terms of something that uses phi. What specifically does this mean? I doubt it's the golden ratio... DS (talk) 17:14, 23 April 2017 (UTC)[reply]

It is defined in Aurifeuillean factorization, although I think the description in the footnote is quite confusing. --mfb (talk) 23:42, 23 April 2017 (UTC)[reply]

I'm pretty sure they're cyclotomic polynomials. Dan Bloch (talk) 19:35, 23 June 2022 (UTC)[reply]

Teraprime, also about the bevaprime name problem[edit]

What if a Teraprime was used to describe primes over 10¹² ? Also, bevaprime is not in use currently, there are no known primes above 24 million digits. YeetPlus (talk) 18:52, 25 September 2020 (UTC)[reply]

Too many primes[edit]

I request only list primes with more than 2,000,000 digits, because there are too many megaprimes nowadays. Thingofme (talk) 01:31, 17 December 2021 (UTC)[reply]

The confirmed primes[edit]

When the primes are confirmed by Prime Pages, sometimes it's still a PRP. Thingofme (talk) 13:56, 13 May 2022 (UTC)[reply]

Splitting out table[edit]

I'm going to split out the table into its own article. I assume this is noncontroversial (the table starts at 2,000,000 digits, not 1,000,000, and megaprime is not a synonym for large prime, as well as not being a widely used term in general). Dan Bloch (talk) 19:29, 21 June 2022 (UTC)[reply]

This is done. Dan Bloch (talk) 21:51, 21 June 2022 (UTC)[reply]