Carmichael numbers are composites such that
, and thus cannot be found to be composite using Fermat's little theorem criterion.
A composite is a Carmichael number if and only if it is squarefree and,
for every prime dividing , divides .
Carmichael numbers must be odd and have at least 3 prime factors.
If for a certain the 3 numbers , and are
prime, then their product is Carmichael number.
The first Carmichael numbers are
561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973 more terms
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
A graph displaying how many Carmichael numbers are multiples of the primes p
from 2 to 71. In black the ideal line 1/p