English

Some Conjectures on the Number of Primes in Certain Intervals

Number Theory 2009-06-02 v1

Abstract

In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture can be proved assuming our improved version of Legendre's Conjecture. Finally, we sharpen the Bertrand's Postulate for prime numbers. Our results are backed by extensive empirical investigation.

Keywords

Cite

@article{arxiv.0906.0104,
  title  = {Some Conjectures on the Number of Primes in Certain Intervals},
  author = {Adway Mitra and Goutam Paul and Ushnish Sarkar},
  journal= {arXiv preprint arXiv:0906.0104},
  year   = {2009}
}

Comments

6 pages, one llncs.cls file

R2 v1 2026-06-21T13:07:59.040Z