TY - JOUR

T1 - Strings of special primes in arithmetic progressions

AU - Monks, Keenan

AU - Peluse, Sarah

AU - Ye, Lynnelle

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2013/9

Y1 - 2013/9

N2 - 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 ⌋.

AB - 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 ⌋.

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U2 - 10.1007/s00013-013-0544-x

DO - 10.1007/s00013-013-0544-x

M3 - Article

AN - SCOPUS:84884290639

VL - 101

SP - 219

EP - 234

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 3

ER -