An Accurate Heuristic for a Problem of Shparlinski. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Pausinger, Florian
• Is Part Of: Experimental mathematics. Volume 26:Issue 1(2017)
• Page Start: 72
• Page End: 76
• Publication Date: 2017-01-02
• Subjects: 11A41 -- 11N13; primes in arithmetic progressions -- Siegel-Walfisz theorem; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2015.1116117
• Languages: English
• ISSNs: 1058-6458

Abstract

ABSTRACT: In this note, we apply classical results from number theory to give an affirmative, but heuristic, answer to the question of Shparlinski (Japanese J. Math., 2012) whether there exist infinitely many primes p of the form p = k 2 + lk + 1, with integers k, l, such that k > 0 and . Based on a heuristic argument, we provide a formula for the number of such primes, which is surprisingly accurate as computations show.