Pseudoprime Cullen and Woodall numbers

Florian Luca, Igor E. Shparlinski
2007 Colloquium Mathematicum  
We show that if a > 1 is any fixed integer, then for a sufficiently large x > 1, the nth Cullen number C n = n2 n + 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 C n 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 W n = n2 n − 1 for all n ≥ 1.
doi:10.4064/cm107-1-5 fatcat:ameoah3aovhl7ggrgawpo25ucy