Strings of special primes in arithmetic progressions

Keenan Monks, Sarah Peluse, Lynnelle Ye

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Green-Tao Theorem, one of the most celebrated theorems in modern number theory, states that there exist arbitrarily long arithmetic progressions of prime numbers. In a related but different direction, a recent theorem of Shiu proves that there exist arbitrarily long strings of consecutive primes that lie in any arithmetic progression that contains infinitely many primes. Using the techniques of Shiu and Maier, this paper generalizes Shiu's Theorem to certain subsets of the primes such as primes of the form ⌊Π n⌋ and some of arithmetic density zero such as primes of the form ⌊ n log log n ⌋.

Original languageEnglish (US)
Pages (from-to)219-234
Number of pages16
JournalArchiv der Mathematik
Volume101
Issue number3
DOIs
StatePublished - Sep 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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