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After I read Paul Jobling's (last but one) posted mail I have re-read my first posted mail
with an algorithm to this forum. Unfortunately I haven't written down a main
thing.

In the fifth step...

Speed up the general k sieve algorithm:
The big trick:

If order(2,p) is divisible by D, where D is an integer then there is only one c(k)
mod D for every remaining k value for that if k*2^n+1...