Explicit interval estimates for prime numbers

Cully-Hugill, Michaela; Lee, Ethan

doi:10.1090/mcom/3719

Explicit interval estimates for prime numbers
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by Michaela Cully-Hugill and Ethan S. Lee HTML | PDF

Math. Comp. 91 (2022), 1955-1970 Request permission

Abstract:

Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of $(\Delta ,x_0)$ such that for all $x \geq x_0$ there exists at least one prime in the interval $(x(1-\Delta ^{-1}),x]$.

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