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 = k2 + lk + 1, with integers k, l, such that k > 0 and 0 ≤ 1 < 2√k + 1. Based on a heuristic argument, we provide a formula for the number of such primes, which is surprisingly accurate as computations show.
Original language | English |
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Pages (from-to) | 72-76 |
Journal | Experimental Mathematics |
Volume | 26 |
Issue number | 1 |
Early online date | 07 Jul 2017 |
DOIs | |
Publication status | Early online date - 07 Jul 2017 |
Keywords
- primes in arithmetic progressions
- Siegel-Walfisz theorem
ASJC Scopus subject areas
- General Mathematics