This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Catalan pseudoprime" – news · newspapers · books · scholar · JSTOR (December 2015) (Learn how and when to remove this template message)

In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence

where Cm denotes the m-th Catalan number. The congruence also holds for every odd prime number n that justifies the name pseudoprimes for composite numbers n satisfying it.

Properties

The only known Catalan pseudoprimes are: 5907, 1194649, and 12327121 (sequence A163209 in the OEIS) with the latter two being squares of Wieferich primes. In general, if p is a Wieferich prime, then p2 is a Catalan pseudoprime.

References