I gave this one to George, he gave a pretty good explanation, but I wanted to see what everyone else thought. I bet He's right, though >primes of the form (s# + 1), (s! +1 ), (k*(s!) +1) or (k*(s#)+1) should make >good exponents, at least in theory. 2^p -1 can be turned into 2^p -2 +1, and >that turns into 2(2^(p-1)-1) + 1 if p is one of the forms above, then this >turns into 2(2^s# -1)+1, 2(2^s!-1)+1 , 2(2^k*(s#)-1)+1 or 2(2^k*(s!)-1) +1. >the 2^s#-1, and related forms must have a lot of factors, like (2^2)-1 , >(2^3)-1 , etc. These are multiplied together, and one is added. This >virtually forms the p# + 1, Euclid formula for showing an infinite number of >primes. I hope you haven't heard this before. If you did tell me. I wonder >who would have discovered this. Probably a great prime hunter of the past. His Response: I'm not really sure how this helps. Factors of Mersenne numbers must be of the form 2kp+1. Apparently, you are looking for special forms of p where more of the 2kp+1 values are composite. An interesting idea, I'll think about it some. Remember, I'm more programmer than mathematician. My Response: >Every Mersenne prime is of the form (2^n -1). If n is composite, with >factors, t and s, the (2^n - 1) is 0 mod (2^t - 1), and (2^s - 1). >So, if n has a lot of factors, like the primorals or the factorials, it >should be divisible by a lot of numbers. If we multiply this by 2 we still >have a number full of factors. If we add 1 to this then the resulting number >is 1 mod all those factors. So, that new number is relatively prime to all >those factors, and so has a good chance of being prime. His response: Your analysis is good as far as it goes. However, we already know that Mersenne numbers have factors of the form 2kp+1. Thus, the factors you eliminated may already have been eliminated by the 2kp + 1 criteria. If that is the case, and I suspect it is, then there is no gain. Anyone want to comment, or give any idea's? Just a little something to cheer up your day. I personally think his suspicions could be confirmed, so it should be (k*2^n) - 1 to help with this, for those of you who are searching for primes other than Merensee's. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
