Optimal depth?

[hhh]

Only if you plan to test all the k/n pairs being sieved. However, in a project like SoB, where a prime found will eliminate a whole k, this is not true.

Or if you take into account that fact into your calculations of the optimal sieve depth. Which I did. Basically: Even after throwing out of the window tons of factors due to the primes found, we are still better off first sieving to 100P and then starting the PRP tests.

Here, you're better off putting your resources into PRP:Sieve at 20:1 ratio and be done with it. Here's the reasoning:

Sieving will make the project 5% faster (assuming the current 25P to future 200P, and zero cost of sieving). How else can we make the project 5% faster? Why, putting 5% more resource in the PRP stage, of course. So if you're using more than 5% of resource on sieving, move it to PRP, and it will achieve the same thing.

You do not define what you mean by faster. Of course, if you don't sieve, at the beginning you are flying through the ranges faster. Later, you realize that you should perhaps sieve a little. But this work would have saved much of your earlier work if it had been done earlier. This is especially true at the current levels where the primes start to be rare.

Admittedly, this is not a thorough analysis of optimality, but it is good enough. People are seriously overestimating the value of sieve, and losing sight of the big picture.

IMO, people love to start crunching and to find the easy primes without proper preparation.

Anyway, there is no way to start a flamewar on this topic. Our little discussion will have no impact whatsoever on the average behaviour. Primegrid is happily sieving, SoB happily PRPing, I think everything is just fine as it is.

H.