2007-06-18, 01:31   #8
Citrix

Jun 2003

5×317 Posts

Quote:
 Originally Posted by jasong I'm going to expose my ignorance here. Because the numbers are of the form k*2^n+1, and k is prime, does this not increase the chance that a number has a small factor like 3 or 5? I mean, with other k's there's an increased chance, an observable phenomenon, that one or more small primes are represented in the k-value. In my opinion, the fact that it's always a prime k decreases the chance that a random n-value will yield a prime. Am I wrong?
Yes you are right. If we were only looking at numbers n==1 (mod 3) then there is an increased chance of finding a chance. A greater chance by 3/2 ie 1.5x more likely.

Using a program I calculated that if you sieve a bunch of numbers to 20M, then each candidate remaining is 30 times more likely to be prime compared to each before sieving.

edit: this is true in general, but if a series has special form of factors like mersenne numbers, then this is totally off. No one knows if prime cullen factors have a special form or not.

Last fiddled with by Citrix on 2007-06-18 at 02:10