Are Legendre symbols proven to be defective?

[jasong]

Okay, I've reread the thread. After being away for a while, and talking to my friend, I decided that I'd stick to the non-math Forums of Mersenne Forum. If I have any math questions, I'm sure there are forums that are more respectful and helpful than this one.

Anyway, I re-read the first 18 posts, and decided that the responses got me a bit over-excited, which confused me. I now agree that 2^3355584+1 is most definitely NOT prime. But that still leaves the problem of the factor of 2. I believe that the bug in NewPGen is that the Verify option should be considered mandatory if someone intends to find ALL primes in a certain range.

I also believe, though I'm not certain, that the use of Legendre symbols, the use that people claim is 100% reliable, causes the obviously incorrect conclusion that 2^3355584+1 is divisible by 2. (assuming I typed the n-value correctly in this case)

[wreck]

Originally Posted by jasong

I now agree that 2^3355584+1 is most definitely NOT prime.

It seems like that you dont know the following fomula
a^n+1 = (a+1)(a^(n-1)-a^(n-2)+...+(-1)^(k-1).a^(n-k)+...+(-1)^(n-1))
when n%2==1

a^n-1 = (a-1)(a^(n-1)+a^(n-2)+...+a^(n-k)+...+1)

and from the first fomula can prove if 2^n+1 is a prime, then n=2^i, where i is a integer.