Mersenne numbers are base-2 pseudoprimes. All would be indicated as prime in P-1 factoring or Fermat PRP tests, whether actually prime or composite. Using 3 as the base provides useful information, and costs no more computing time; using 2 as the base provides no useful information. That's a summary of my understanding of
this thread as it relates to base choice.
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https://www.mersenneforum.org/showth...736#post510736
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