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arXiv · 1908.08613

Large prime gaps and probabilistic models

William Banks·Kevin Ford·Terence Tao
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Abstract

We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we obtain heuristic upper and lower bounds for the size of the largest prime gap in the interval $[1,x]$. Our results are stated in terms of the extremal bounds in the interval sieve problem. The same methods also allow us to rigorously relate the validity of the Hardy-Littlewood conjectures for an arbitrary set (such as the actual primes) to lower bounds for the largest gaps within that set.

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William Banks, Kevin Ford, Terence Tao. 2019-08-22. Large prime gaps and probabilistic models. https://arxiv.org/abs/1908.08613

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