Well spaced integers generated by an infinite set of primes

Kim, Jeongsoo; Stewart, C.

doi:10.1090/S0002-9939-2014-11979-4

Well spaced integers generated by an infinite set of primes
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by Jeongsoo Kim and C. L. Stewart PDF

Proc. Amer. Math. Soc. 143 (2015), 915-923 Request permission

Abstract:

In this article we prove that there exists an infinite set of prime numbers with the property that the sequence $1=n_1<n_2<\cdots$ of positive integers made up of primes from the set is well spaced. For example we prove that there is an infinite set of prime numbers for which \begin{equation*} n_{i+1}-n_i>n_i/\exp ((\log n_i)^{1/2}) \end{equation*} for $i=1,2,\dots$.

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