Golomb's conjecture on prime gaps

2016/04/23 by Christian Elsholtz, Elsholtz, Christian
Mathematics · #11A41 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A41

paper · pdf · doi:10.48550/arxiv.1604.06903

arxiv created 2016/04/23 · arxiv updated 2016/04/26

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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