- Properties
- References
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 {{OEIS|A163209}} with the latter two being squares of Wieferich primes. In general, if p is a Wieferich prime, then p2 is a Catalan pseudoprime.
References
- {{cite journal | last1 = Aebi | first1 = C. | last2 = Cairns |first2 = G. | title = Catalan numbers, primes and twin primes
| journal = Elemente der Mathematik |volume=63 |issue=4 | pages = 153–164 | year = 2008 | url = http://gradelle.educanet2.ch/christian.aebi/.ws_gen/9/catalan.pdf | doi = 10.4171/EM/103}}
- Catalan pseudoprimes. Research in Scientific Computing in Undergraduate Education.
1 : Pseudoprimes
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