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arXiv · 1407.7324

Some Notes on Digit Strings in the Primes

Adrian Dudek
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Abstract

Let $S$ be a string of $l$ decimal digits. We give an explicit upper bound on some prime $p$ whose decimal representation contains the string $S$. We also show, as a corollary of the Green-Tao theorem, that there are arbitrarily long arithmetic progressions of prime numbers all of whose decimal representations contain $S$.

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Adrian Dudek. 2014-07-30. Some Notes on Digit Strings in the Primes. https://arxiv.org/abs/1407.7324

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