# Talk:Megaprime

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Field: Number theory

## 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)