A Part of Oppermann’s Conjecture, Legendre’s Conjecture and Andrica’s Conjecture

Abstract

In this paper we discuss a part of Oppermann’s Conjecture ”there is at least two primes between n2 − n to n2 and at least another two primes between n^2 to n^2+ n for n≥3.5×〖10〗^6 ”. A part of Legendre’s Conjecture ”there is at least two primes between n^2 to 〖(n+1)〗^2 for n ≥3.5×〖10〗^6 ” and a part of Andrica’s Conjecture states that ” √(p_(n+1) )− √(p_n ) < 1 for every pair of consecutive prime numbers p_n and p_(n+1) (of course, p_n< p_(n+1) ) for n≥3.5×〖10〗^6”. We propose a conjecture regarding the distribution of prime numbers.