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arXiv · 0706.0889

Expected gaps between prime numbers

Fred B. Holt
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Abstract

We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations. Using this recursion we can estimate the numbers of a gap or of a constellation that occur between a prime and its square. This recursion also has explicit implications for open questions about gaps between prime numbers, including three questions posed by Erdös and Turán.

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Fred B. Holt. 2007-06-06. Expected gaps between prime numbers. https://arxiv.org/abs/0706.0889

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