Concept
Fermat's little theorem states that if p is prime and, then
If we want to test if p is prime, then we can pick random a's in the interval and see if the equality holds. If the equality does not hold for a value of a, then p is composite. If the equality does hold for many values of a, then we can say that p is probable prime.
It might be in our tests that we do not pick any value for a such that the equality fails. Any a such that
when n is composite is known as a Fermat liar. Vice versa, in this case n is called Fermat pseudoprime to base a.
If we do pick an a such that
then a is known as a Fermat witness for the compositeness of n.
Read more about this topic: Fermat Primality Test
Famous quotes containing the word concept:
“Jesus abolished the very concept of “guilt”Mhe denied any cleavage between God and man. He lived this unity of God and man as his “glad tidings” ... and not as a prerogative!”
—Friedrich Nietzsche (1844–1900)
“The two most far-reaching critical theories at the beginning of the latest phase of industrial society were those of Marx and Freud. Marx showed the moving powers and the conflicts in the social-historical process. Freud aimed at the critical uncovering of the inner conflicts. Both worked for the liberation of man, even though Marx’s concept was more comprehensive and less time-bound than Freud’s.”
—Erich Fromm (1900–1980)
“Terror is as much a part of the concept of truth as runniness is of the concept of jam. We wouldn’t like jam if it didn’t, by its very nature, ooze. We wouldn’t like truth if it wasn’t sticky, if, from time to time, it didn’t ooze blood.”
—Jean Baudrillard (b. 1929)