Open Access
Translator Disclaimer
2011 Frequencies of Successive Pairs of Prime Residues
Avner Ash, Laura Beltis, Robert Gross, Warren Sinnott
Experiment. Math. 20(4): 400-411 (2011).

Abstract

We consider statistical properties of the sequence of ordered pairs obtained by taking the sequence of prime numbers and reducing modulo $m$. Using an inclusion/exclusion argument and a cutoff of an infinite product suggested by Pólya, we obtain a heuristic formula for the "probability" that a pair of consecutive prime numbers of size approximately $x$ will be congruent to $(a, a + d)$ modulo $m$. We demonstrate some symmetries of our formula. We test our formula and some of its consequences against data for $x$ in various ranges.

Citation

Download Citation

Avner Ash. Laura Beltis. Robert Gross. Warren Sinnott. "Frequencies of Successive Pairs of Prime Residues." Experiment. Math. 20 (4) 400 - 411, 2011.

Information

Published: 2011
First available in Project Euclid: 8 December 2011

zbMATH: 1269.11096
MathSciNet: MR2859898

Subjects:
Primary: 11K45 , 11N05 , 11N69

Keywords: Bateman–Horn , Hardy–Littlewood , Pólya , Prime pairs

Rights: Copyright © 2011 A K Peters, Ltd.

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.20 • No. 4 • 2011
Back to Top