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] |
The following theorem might help :
Fermat, a French mathematician, once proved that : " If p is a prime number whilst GCD(p,a)==1 then ap-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=2p-1 is prime if and only if 2p-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...
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