Some Conjectures on the Number of Primes in Certain Intervals

Details Some Conjectures on the Number of Primes in Certain Intervals Some Conjectures on the Number of Primes in Certain Intervals

2009-05-30

arxiv.org/abs/0906.0104v1

Mathematics

Number Theory

6 pages, one llncs.cls file

Scientific paper

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.

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