In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence
where Cm denotes the m-th Catalan number.
The above congruence holds for every odd prime number n, so any composite n that satisfies it is pseudoprime.
Properties
The only known Catalan pseudoprimes are: 5907, 1194649, and 12327121 with the latter two being squares of Wieferich primes. In general, if p is a Wieferich prime, then p2 is a Catalan pseudoprime.
References
Catalan pseudoprimes. Research in Scientific Computing in Undergraduate Education.