## Carmichael numberAlso known as an absolute pseudoprime, a number n
that is a Fermat pseudoprime to any
base, i.e., it divides (a^{n}
- a) for any a. Another way of saying this is that a Carmichael
number is actually a composite number
even though Fermat's little theorem
suggests it is probably a prime number.
(Fermat's little theorem says that if P is a prime number then
for any number a, (a^{P} - a)
must be divisible by P. Carmichael numbers satisfy this condition to any
base despite being composite.) There are only seven Carmichael numbers under 10,000 – 561, 1105, 1729, 2465, 2821, 6601, and 8911 – and less than a quarter of a million of them under 10 ^{16}. Nevertheless, in 1994 it was proved that
there are infinitely many of them. All Carmichael numbers are the product
of at least three distinct primes, for example, 561 = 3 × 11 × 17. ## Related category• TYPES OF NUMBERS | |||||

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