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arXiv · 1604.06903

Golomb's conjecture on prime gaps

Christian Elsholtz
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Abstract

Question 10208b (1992) of the American Mathematical Monthly asked: does there exist an increasing sequence $\{a_k\}$ of positive integers and a constant $B > 0$ having the property that $\{ a_k + n\}$ contains no more than $B$ primes for every integer $n$? A positive answer to this question became known as Golomb's conjecture. In this note we give a negative answer, making use of recent progress in prime number theory.

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Christian Elsholtz. 2016-04-23. Golomb's conjecture on prime gaps. https://arxiv.org/abs/1604.06903

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