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 2016-04-23, 18:29 #5 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 59×157 Posts 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.