Original scientific paper

https://doi.org/10.3336/gm.53.1.01

New upper bounds for Ramanujan primes

Anitha Srinivasan ; Saint Louis University - Madrid Campus, Avenida del Valle 34, 28003 Madrid, Spain
Pablo Ares-Gastesi ; Department of Applied Mathematics and Statistics, School of Business and Economics, Universidad CEU San Pablo, Madrid, Spain

Abstract

For n≥ 1, the nth Ramanujan prime is defined as the smallest positive integer Rn such that for all x≥ Rn, the interval (x/2, x] has at least n primes. We show that for every ε>0, there is a positive integer N such that if α=2n(1+(log 2+ε)/(log n+j(n))), then Rn< p[α] for all n>N, where pi is the ith prime and j(n)>0 is any function that satisfies j(n)→ ∞ and nj'(n)→ 0.

Keywords

Ramanujan primes; upper bounds

Hrčak ID:

201806

URI

https://hrcak.srce.hr/201806

Publication date:

20.6.2018.

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