Re: Re: Finding Primes

Hi Abigail,

You're quite right but I never actually meant to give a solution to the 200-digit long number, I was only recapping the typical algorithms one can come up with, pretenselessly ;-)...
There must be an option with n! numbers because they grow so quickly - I thought that n!+1 might a prime number but an easy counter-example is n=4 (which'd give n!=24 hence n!+1=25 = 5*5, barely what you can call a prime number...)

Comment on Re: Re: Finding Primes

Replies are listed 'Best First'.
Re: Finding Primes by Abigail-II (Bishop) on Aug 14, 2003 at 11:03 UTC
The only thing you can say about `n! + 1` is that it will only contain prime factors that are larger than `n`. And that the series `(n! + 2) .. (n! + n)` will not contain a prime number. Abigail	[reply]
Re: Re: Finding Primes : Fermat's "small" theorem by Foggy Bottoms (Monk) on Aug 14, 2003 at 13:17 UTC
The following theorem might help : Fermat, a French mathematician, once proved that : " If p is a prime number whilst GCD(p,a)==1 then a^p-1 is congruous to 1 modulo p." But actually this theorem isn't enough, it helps you prove a number is not prime, not the other way round... Lucas, another French dude, came up with yet another theorem which looks for Mersenne's prime numbers : Given p an odd number, the number M=2^p-1 is prime if and only if 2^p-1 divides S(p-1) where S(n+1)=S(n)² - 2, and S(1) = 4. Further down the road, Indian scientists came up with a very interesting paper you may want to check out : they probably have an answer to your problem : <a href=http://www.cse.iitk.ac.in/news/primality.pdf>primality.pdf</a>... Hopefully, I've been of some help - maths are really interesting and I always enjoy digging into them...	[reply]