561 (five hundred [and] sixty-one) is the natural number following 560 and preceding 562.
In mathematics 561 is a Fermat pseudoprime to base 2, a centered icosahedral number, the 33rd triangular number, and the 17th hexagonal number. It is a composite number, with the divisors being 1, 3, 11, 17, 33, 51, 187, and 561. Its prime factorization is 3 * 11 * 17.
Carmichael number 561 is most notable for being the first, and smallest Carmichael number. 561 is considered one since it satisfies the Korselt’s Criterion. A number satisfies the criterion if the number is an odd number, consists of a product of distinct primes, and satisfies (p − 1) | (n − 1) for every prime p dividing the number. It was first discovered by Václav Šimerka along with six more other numbers.
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