Catalan pseudoprime

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.

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.