In number theory, a probable prime (PRP) is an integer that satisfies a specific condition also satisfied by all prime numbers. Different types of probable primes have different specific conditions. While there may be probable primes that are composite (called pseudoprimes), the condition is generally chosen in order to make such exceptions rare.
Fermat's test for compositeness, which is based on Fermat's little theorem, works as follows: given an integer n, choose some integer a coprime to n and calculate an − 1 modulo n. If the result is different from 1, n is composite. If it is 1, n may or may not be prime; n is then called a (weak) probable prime to base a.
Other articles related to "probable prime, prime":
... An Euler probable prime to base a is an integer that is indicated prime by the somewhat stronger theorem that for any prime p, a(p − 1)/2 equals modulo p, where is ... An Euler probable prime which is composite is called an Euler–Jacobi pseudoprime to base a ... using the fact that the only square roots of 1 modulo a prime are 1 and −1 ...
Famous quotes containing the words prime and/or probable:
“My prime of youth is but a frost of cares,
My feast of joy is but a dish of pain,
My crop of corn is but a field of tares,
And all my good is but vain hope of gain:
The day is past, and yet I saw no sun,
And now I live, and now my life is done.”
—Chidiock Tichborne (15581586)
“I have very lately read the Prince of Abyssinia [Samuel Johnsons Rasselas]MI am almost equally charmed and shocked at itthe style, the sentiments are inimitablebut the subject is dreadfuland, handled as it is by Dr. Johnson, might make any young, perhaps old, person trembleO heavens! how dreadful, how terrible it is to be told by a man of his genius and knowledge, in so affectingly probable a manner, that true, real happiness is ever unattainable in this world!”
—Frances Burney (17521840)