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Old 2020-10-19, 00:05   #3
charybdis's Avatar
Apr 2020

26610 Posts

Originally Posted by VBCurtis View Post
I've wondered about this also, though my curiosity was about cofactors slightly bigger than 2*mfb but still too small to possibly split into 3 large primes.
CADO definitely deals with these properly - see this snippet from sieve/las-cofactor.cpp:

  nd = mpz_get_d (n);
  B = (double) scs.lim;
  kB = B * B;
  for (klpb = lpb; klpb < s; klpb += lpb, kB *= B)
      /* invariant: klpb = k * lpb, kB = B^(k+1) */
      if (nd < kB) /* L^k < n < B^(k+1) */
	return 0;
I couldn't find anything related to the double large prime bound, but there's a LOT of code for the siever so there's every chance I just haven't found it.
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