Vol. 8, No. 2, 2015
Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 723–899
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
On the least prime congruent to 1 modulo $n$

Jackson S. Morrow

Vol. 8 (2015), No. 2, 357–359
DOI: 10.2140/involve.2015.8.357
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