Expected gaps between prime numbers

Details Expected gaps between prime numbers Expected gaps between prime numbers

2007-06-06

arxiv.org/abs/0706.0889v1

Mathematics

Number Theory

21 pages, LaTeX, 2 pdf figures

Scientific paper

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 Erd\"os and Tur\'an.

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