Acceleration detection of large (probably) prime numbers
This work addresses a specific, incremental optimization for practitioners who need to generate large probable primes efficiently, though it is noted as irrelevant to theoretical research.
The paper tackles the problem of accelerating the detection of large probable prime numbers by determining the optimal stopping point for trial division before applying the Miller-Rabin algorithm, resulting in a practical solution that reduces computational time for users generating such numbers.
In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resort to trial division by a few initial prime numbers, since such a division take less time. How far we should go with such a division is the that we are trying to answer in this paper?For the theory of the matter is fully resolved. However, that in practice we do not have much use. Therefore, we present a solution that is probably irrelevant to theorists, but it is very useful to people who have spent many nights to produce large (probably) prime numbers using its own software.