Quote:
Originally Posted by Prime95
All prime factors will be tested. A small nondeterministic set of composite factors will also be tested.

Hmm.
Is this nondeterministic set of composite factors a problem for Gerbicz' TF proof of work method?
https://www.mersenneforum.org/showpo...7&postcount=30 If for the set of q=2kp+1 that are composite but are not sieved out, one or more of (Mp mod q) mod 2
^{t} is 1, it would seem so. Testing in that case that a candidate k for the proof list gives a prime q (finishing the sieving of only those that are candidates to go into the verification list) should handle that. Maybe that's best done on the cpu. The value of the list formed, as a proof of work, is that it is hard to produce, and easy to verify, rather like a found factor. Also it is usable in the most common TF case, no factor found. And depends on doing most of the actual TF work. And can be made reliable yet somewhat compact in size. And does not depend on keeping secrets such as encryption codes secret.
One of the reasons I like the Gerbicz double mod method is something analogous might be usable for P1 verification of work, which is also not currently present. Some fraction of the code could be reused.