Acceleration detection of large (probably) prime numbers

TL;DR

This paper proposes an efficient method for early detection of large prime numbers by optimizing trial division limits, reducing unnecessary Miller-Rabin tests in practical applications.

Contribution

It provides a practical solution for determining the optimal division range to quickly identify probable primes, aiding software that generates large primes.

Findings

Trial division can effectively filter out non-primes before Miller-Rabin.

The proposed method improves the efficiency of prime testing in large number generation.

Practical implementation benefits prime-searching software by saving computational resources.

Abstract

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.