Currently PsiEval uses Jaeschke's algorithm to compute pseudoprimes of the form p*(2p-1) to the first k prime witnesses. This is sufficient for integers less than 2^128, since the size of the ring 4p#15 is large enough, that with typical parallelism, it is likely optimal for that interval. However, extending beyond 2^128 will require Zhang's algorithm since we want to keep the ring less than 2^64 while minimizing the candidates we check.
Of note is that the current implementation is 118x faster than Zhang's algorithm but this is a combination of weaker hardware, and probably inefficient arithmetic on Zhang's part. It is unclear how much faster an efficient implementation of Zhang's algorithm would be.
Currently PsiEval uses Jaeschke's algorithm to compute pseudoprimes of the form p*(2p-1) to the first k prime witnesses. This is sufficient for integers less than 2^128, since the size of the ring 4p#15 is large enough, that with typical parallelism, it is likely optimal for that interval. However, extending beyond 2^128 will require Zhang's algorithm since we want to keep the ring less than 2^64 while minimizing the candidates we check.
Of note is that the current implementation is 118x faster than Zhang's algorithm but this is a combination of weaker hardware, and probably inefficient arithmetic on Zhang's part. It is unclear how much faster an efficient implementation of Zhang's algorithm would be.