Fermat pseudoprimes
Acta Arithmetica
MSC: Primary 11A51; Secondary 11N25, 11N32, 11Y11
DOI: 10.4064/aa250411-9-10
Published online: 29 December 2025
Abstract
We give an upper bound for the distribution of base-$a$ pseudoprimes that is uniform in the base and does not require coprimality to the base. In addition we show that there are infinitely many “near Carmichael numbers” meaning that they are pseudoprimes for a positive proportion of bases, but not all bases.
