--- In

primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:

> Please see my draft paper at:

> http://www.mersenneforum.org/showpost.php?p=298027&postcount=44

> (Ignore the the mix up I made with the comparison between FFT multiplication and FFT squaring timings.)

>

> The 2.X selfridge composite test I have there has been tested to 4*10^12. I am planning to get to 10^14 in a core year, with the help of a prp-sieve written by Jens K. Anderson. I would go to 10^15 if my resources were not elsewhere employed.

>

I should say that the program by Jen K. Andersen is a "psp-sieve" -- it generates a list of pseudoprimes for a given base and range, where gcd(base,n)==1. For instance, I can pre-screen my test

(2+L)^(n+1)==5 (mod n, L^2+1) with output from Jens program for base 5:

5^(n+1)==25 (mod n).

This takes care of about half the throughput.

I then repeat the process for odd bases 7,...,29. This greatly reduces the amount of work my program has to do; It can then ignore the case where x<(31-5)/2 and gcd(base,n)==1

Paul