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Erdős Problem #4 — Lower bounds for large gaps between consecutive primes

Erdős

For every c>0c>0, there are infinitely many indices nn such that

pn+1−pn>c log⁡n log⁡log⁡n log⁡log⁡log⁡log⁡n(log⁡log⁡log⁡n)2.p_{n+1}-p_n>c\,\frac{\log n\,\log\log n\,\log\log\log\log n}{\left(\log\log\log n\right)^2}.
Sources & referencesView supporting material

Primary source

P. Erdős, Some recent advances and current problems in number theory, Lectures on Modern Mathematics III, Wiley (1965), 196-244.

erdos-problemnumber-theoryprimes

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