Editing Primality test (section)

== Number-theoretic methods ==
Certain number-theoretic methods exist for testing whether a number is prime, such as the [[Lucas primality test|Lucas test]] and [[Proth's theorem|Proth's test]]. These tests typically require factorization of ''n''&nbsp;+&nbsp;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.