Quick TF Question

[Dubslow]

For a given bit level, how many factors does mfaktc test? How many are sieved out, (SievesPrimes=5000) and then how many are actually tested on the GPU?

[Christenson]

For a given mersenne exponent p, all factors will be primes of the form 2*k*p+1, for some k. You can calculate how many candidates that would be, given p and the bit levels.

The second thing you can do is to use the prime density function to estimate how many of those 2*k*p+1 are actually prime. SievePrimes indicates that the CPU ensured that the first SievePrimes primes do not factor the candidates passed to your GPU for checking to see if 2^p-1 mod 2*k*p+1 is in fact zero.

To a first order, the number of primes between 2^m and 2^m+1 is the integral from 2^m to 2^m+1 of 1/ln(x). That is, using a trapezoidal approximation, 2^m * [1/ln(2^m) + 1/ln(2^m+1)]/2.

Multiply this by the number of candidates/2^m to get the approximate number of factor candidates sent to the GPU.

If you want the exact number, mfaktc reports how many candidates it sends to the GPU for each class. You can do the division to see for yourself the large fraction that got sieved out.

[Dubslow]

Originally Posted by Christenson

For a given mersenne exponent p, all factors will be primes of the form 2*k*p+1, for some k. You can calculate how many candidates that would be, given p and the bit levels.

The second thing you can do is to use the prime density function to estimate how many of those 2*k*p+1 are actually prime. SievePrimes indicates that the CPU ensured that the first SievePrimes primes do not factor the candidates passed to your GPU for checking to see if 2^p-1 mod 2*k*p+1 is in fact zero.

To a first order, the number of primes between 2^m and 2^m+1 is the integral from 2^m to 2^m+1 of 1/ln(x). That is, using a trapezoidal approximation, 2^m * [1/ln(2^m) + 1/ln(2^m+1)]/2.

Multiply this by the number of candidates/2^m to get the approximate number of factor candidates sent to the GPU.

If you want the exact number, mfaktc reports how many candidates it sends to the GPU for each class. You can do the division to see for yourself the large fraction that got sieved out.

Where does it report that?
Edit: Candidates, right? That's per class?