Characterization of prime and composite numbers using the notion of successive sum of integers and the consequence in primality testing

In this paper, we give a characterization of primes and composite natural numbers using the notion of the sum of successive natural numbers. We prove essentially that an odd natural number N ≥ 3 is prime if and only if the unique decomposition of N as a sum of successive natural numbers is the trivial decomposition N = a + (a + 1) with a = (N - 1) / 2.