Towards Proving Legendre's Conjecture
| dc.creator | Kintali, Shiva | |
| dc.date | 2008-11-26 | |
| dc.date | 2009-01-11 | |
| dc.date.accessioned | 2026-07-07T12:27:47Z | |
| dc.date.available | 2026-07-07T12:27:47Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0811.4451 | |
| dc.identifier | http://arxiv.org/abs/0811.4451 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215328 | |
| dc.subject | Number Theory | |
| dc.title | Towards Proving Legendre's Conjecture | |
| dc.type | text |