An Accurate Heuristic for a Problem of Shparlinski

Florian Pausinger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)72-76
JournalExperimental Mathematics
Issue number1
Early online date07 Jul 2017
Publication statusEarly online date - 07 Jul 2017


  • primes in arithmetic progressions
  • Siegel-Walfisz theorem

ASJC Scopus subject areas

  • Mathematics(all)


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