Pseudoprime Cullen and Woodall numbers

Florian Luca, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We show that if a > 1 is any fixed integer, then for a sufficiently large x > 1, the nth Cullen number Cn = n2n + 1 is a base a pseudoprime only for at most O(x log log x/log x) positive integers n ≤ x. This complements a result of E. Heppner which asserts that Cn is prime for at most O(x/log x) of positive integers n ≤ x. We also prove a similar result concerning the pseudoprimality to base a of the Woodall numbers given by Wn = n2n − 1 for all n ≥ 1.

Original languageEnglish
Pages (from-to)35-43
Number of pages9
JournalColloquium Mathematicum
Issue number1
Publication statusPublished - 2007


  • Cullen number
  • Pseudoprime number
  • Woodall number


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