Quote:
Originally Posted by Templus
This k you are testing is a quite heavy one! For k*2^n+/1, each choice for k has a certain weight, or: the numbers that remain after sieving.
Resieving will not help: sieving is the process to determine which numbers are divisible by a certain numer (in NewPGen, this is 'p'). So all values for 'n' that are divisible by a number 'p', will also be divisible by that same value for 'p' the next time.
As I see it: you (by accident) chose a k that has a very large weight, so nonprimes are not easily detected by sieving. I recommend you to stop sieving.
If I am mistaken, please correct me!

Roughly speaking, ks with high weight prefer to be sieved more deeply. This is because the each new prime you sieve with is more likely to remove a remaining candidate compared to a k where small primes have already removed a large proportion of the candidates. This implies that candidate removal times will tend to stay higher with heavy k, and so you'll stop sieving later, and so get a marginally better prime/test ratio from the testing phase.
Phil