@OP:
Let me try to make clear what your claim is, in math terms.
You claim:
1. you have a function from primes to booleans (i.e. {true, false}), that is defined as: \(f:P\rightarrow B\) such as \(f(p)=T\) whenever \(2^p1\) is in \(P\) (i.e is prime) and \(f(p)=F\) otherwise.
2. you tested this function for all primes up to \(p=1\, 257\, 787\) and you didn't get any wrong result (neither false positive, nor false negative)
3. this function of yours can be calculated faster than the LL test
Is that really what you are claiming?
You must be careful with the third point, testing all exponents lower than the exponent of M34 (which is 1257787) is VERY fast with the known algorithms, there are a lot of exponents there, but they are really small... One average computer will need about 34 hours to complete all these tests. All together, not each. And using pari/gp, which is very slow, I do not talk here of specialized tools like P95 or so. Did your "formula" take less amount of time?
Last fiddled with by LaurV on 20171228 at 07:08
