Vol. 8, No. 2, 2015

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On the least prime congruent to 1 modulo $n$

Jackson S. Morrow

Vol. 8 (2015), No. 2, 357–359
Abstract

For any integer n > 1, there are infinitely many primes congruent to 1(modn). In this note, the elementary argument of Thangadurai and Vatwani is modified to improve their upper estimate of the least such prime when n itself is a prime greater than or equal to 5.

Keywords
primes in progressions, arithmetic progressions
Mathematical Subject Classification 2010
Primary: 11B25, 11N13
Milestones
Received: 28 November 2013
Revised: 9 March 2014
Accepted: 20 March 2014
Published: 3 March 2015

Communicated by Kenneth S. Berenhaut
Authors
Jackson S. Morrow
Emory University
Druid Hills, GA 30306
United States