Notes on Sophie Germain Primes

Abstract

In this paper, a pair of Sophie Germain prime and connected safe prime is referred to as S G-S -primepair in short. We focus on a characterization to obtain S G-S -prime pairs owing to an eliminating method. We formsome certain instructions for a sieve as an elementary method to find the S G-S -prime pairs and we also give anexample in which we use our instructions to obtain the S G-S -prime pairs up to 250.Wilson’s fundamental theorem in number theory gives a characterization of prime numbers via a congruence. Moreover, in this paper, we give a characterization of Sophie Germain primes via a congruence.