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Explicit Interval Estimates for Prime Numbers

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arxiv 2103.05986 v3 pith:TXJ2J6JP submitted 2021-03-10 math.NT

Michaela Cully-Hugill , Ethan S. Lee This is my paper · ORCID
classification math.NT
keywords deltaintervalprimecomputeestimatesexistsexplicitfunction
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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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  1. Effective short intervals containing primes

    math.NT 2025-08 conditional novelty 5.0 of 10

    For every n ≥ 106 and every x ≥ 1, there is always a prime in the interval [x, x + x^(1−1/n)], making several classical prime-gap results fully explicit.

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