%0 Journal Article
%T Towards Proving Legendre's Conjecture
%A Shiva Kintali
%J Mathematics
%D 2008
%I arXiv
%X Legendre's conjecture states that there is a prime number between n^2 and (n+1)^2 for every positive integer n. We consider the following question : for all integer n>1 and a fixed integer k<=n does there exist a prime number such that kn < p < (k+1)n ? Bertrand-Chebyshev theorem answers this question affirmatively for k=1. A positive answer for k=n would prove Legendre's conjecture. In this paper, we show that one can determine explicitly a number N(k) such that for all n >= N(k), there is at least one prime between kn and (k+1)n. Our proof is based on Erdos's proof of Bertrand-Chebyshev theorem and uses elementary combinatorial techniques without appealing to the prime number theorem.
%U http://arxiv.org/abs/0811.4451v2