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| 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.