Hassani, Mehdi and Sariolgalam, Narges (2004) A Note on Short Intervals Containing Primes. Research report collection, 7 (3).

Abstract

In 1999, P. Dusart showed that for x ≥ 3275, there exists at least a prime number in the interval (x, x(1 + 1/(2ln²x))] and in 2003, O. Ramaré and Y. Saouter showed that for x ≥ 10726905041 there exists at least a prime number in the interval (x(1 − ∆⁻¹), x], in which ∆ = 28314000. In this note, we show that for x ≥ 1.17×10¹⁶³⁴, we can yield Ramaré-Saouter’s result from Dusart’s result.

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