Quote:
Originally Posted by sweety439
Well, you said these conjectures would have to have multiple and separate sieves done (see your post https://mersenneforum.org/showpost.p...&postcount=243), however, you can use srsieve to sieve the sequence k*b^n+1 for primes p not dividing gcd(k+1,b1), and initialized the list of candidates to not include n for which there is some prime p dividing gcd(k+1,b1) for which p dividing (k*b^n+1)/gcd(k+1,b1) (like we can initialized the list of candidates to not include n for which k*b^n+1 has algebra factors, e.g. for square k's for k*b^n1, we can remove all even n in the sieve file, and for cube k's for k*b^n1 and k*b^n+1, we can remove all n divisible by 3 in the sieve file)

In fact, for Sierpinski/Riesel base b, we can use srsieve to sieve the sequence k*b^n+1 for primes p not dividing b1 (since gcd(k*b^n+1,b1) = gcd(k+1,b1) for all n), and initialized the list of candidates to not include n for which there is some prime p dividing b1 for which p dividing (k*b^n+1)/gcd(k+1,b1)