Sieving very thin sets of primes, and pratt trees with missing primes

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that is a set of primes, such that for every, every prime factor of p-1 is also in. We apply a new sieve method to show that either contains all of the primes or the counting function of is O(x1-c) for some c>0, where c depends only on the smallest prime not in. Our proof makes use of results connected with Artin's primitive root conjecture.

Original languageEnglish (US)
Pages (from-to)2955-2971
Number of pages17
JournalInternational Mathematics Research Notices
Volume2014
Issue number11
DOIs
StatePublished - 2014

ASJC Scopus subject areas

  • Mathematics(all)

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