On Mon, 11 Apr 1994, Matthew J Ghio wrote:
Well, for the mathematically curious, here are a few other interesting prime number theroms:
For any number n which is prime, (2^n)-1 is also prime (Mersenne's theorem).
For any number n (2^(2^n))+1 is prime. (I might have that wrong, I don't remember exactly)
For any number n, if the square root of (n!)+1 is an integer, it is also prime. (This is interesting, but rather useless in practice)
This is not "quite true" 1) for (2^n)-1 to be prime, it is indeed necessary that n is prime (if n=pq then 2^p-1 divides 2^n-1) however (2^n)-1 is not prime for all prime n prime numbers of the form 2^n-1 are called Mersenne primes there are some 30 known Mersenne primes for the moment (could send interested people a list of the ones I know--see also Knuth, volume 2 for some interesting stuff about primes) 2) (2^(2^n))+1 is certainly not true for all n, though I don't know any particularly values for which it doesn't hold (I thought 2^128+1 was NOT a prime) primes numbers who happen to be of the form (2^(2^n))+1 are called Fermat primes. Some pretty large ones are known (could send a list...) 3) I don't know about the third stated formula Hope this straightens things out... Frank.Vernaillen@rug.ac.be