Number-theoretic Methods
Certain number-theoretic methods exist for testing whether a number is prime, such as the Lucas test and Proth's test. These tests typically require factorization of n + 1, n − 1, or a similar quantity, which means that they are not useful for general-purpose primality testing, but they are often quite powerful when the tested number n is known to have a special form.
The Lucas test relies on the fact that the multiplicative order of a number a modulo n is n − 1 for a prime n when a is a primitive root modulo n. If we can show a is primitive for n, we can show n is prime.
Read more about this topic: Primality Test
Famous quotes containing the word methods:
“Crime is terribly revealing. Try and vary your methods as you will, your tastes, your habits, your attitude of mind, and your soul is revealed by your actions.”
—Agatha Christie (1891–1976)