Talk:Megaprime

Bevaprime?

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)

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

Bevaprime problem

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)

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)

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)

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

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)

? 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)

Does this page only list primes or also PRPs?

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)

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)

File:Megaprime found.png

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)

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)

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

Phi

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)

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)

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

Teraprime, also about the bevaprime name problem

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)

Too many primes

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)

The confirmed primes

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

Splitting out table

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)

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