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:
“The concept is interesting: to see, as though reflected
In streaming windowpanes, the look of others through
Their own eyes.”
—John Ashbery (b. 1927)
“There is a concept that is the corrupter and destroyer of all others. I speak not of Evil, whose limited empire is that of ethics; I speak of the infinite.”
—Jorge Luis Borges (1899–1986)
“Teaching Black Studies, I find that students are quick to label a black person who has grown up in a predominantly white setting and attended similar schools as “not black enough.” ...Our concept of black experience has been too narrow and constricting.”
—bell hooks (b. c. 1955)