An Efficient Algorithm to Find All Primes in A Given Interval

Abstract

In this paper, we propose a deterministic algorithm for primality testing and primes search in a given integer interval. The algorithm use a new primality test method, which replace modulo operator with elementary arithmetic operations, hence a better efficiency than divisibility test. The algorithm is working; it generates a prime base by an expansion process and is appropriate for a fast search for small primes (a dozen of digits). We propose a filtering method to overcome memory constraints, and use the algorithm to expand much more the prime base and find medium size primes (dozens of digits).