Primes and consecutive sums in arithmetic progressions

Abstract

A necessary and sufficient condition for a positive integer to be prime is explored in terms of its number-theoretic ramifications and its generalization to arithmetic progressions. A computer experiment is shown describing how the main results were conjectured. Several open problems are posed for readers.

Keywords:

• Prime
• arithmetic progression
• multiplicative function
• RSA cryptosystem
• unique factorization
• computer experiment

C.R Categories:

• F.2.1
• G.m
• H.1