Optimal depth?

[Joe O]

To make sure I'm understanding this correctly: sieving saves time because it finds factors, making it unnecessary to run the proth test on that number. Also, at this point, sieving is eliminating n faster than proth tests are. The optimal sieve depth is the point at which sieving removes candidates at the same rate as proth tests. Are these statements accurate?

More or less!
Since we are running 2 proth tests on most k n pairs, you could argue that the optimal sieving depth is the point at which sieving removes candidates at half the rate that proth tests do.