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Old 2016-04-23, 18:29   #5
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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I am not sure people usually think about these things but I suppose this place to cast them is as good as any:
  • Suppose one has a great sieve (note: I am not talking about 10% faster, or even 50%; let's say 10x faster or better 1000000x faster. Hint: significant restriction on factors)
  • Then one will sieve perhaps much deeper, not just to Ts, or even Ps, but into Es.
  • That's great! There will be 20-50% less candidates left after such a great sieve compared to "some other form"
  • ...Now, the form has to be searchable at least equally fast as, say, Proths/Riesels. Is this achievable?
  • - No! Except for very carefully researched forms. b>2 (but not GFN) is slower, |c| \ne 1 is significantly slower.
  • Ergo: when people search for such primes they (hopefully) know that they are deliberately searching for "slow", hard, but exotic primes.
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