Search results
Results from the WOW.Com Content Network
The simplest primality test is trial division: given an input number, , check whether it is divisible by any prime number between 2 and (i.e., whether the division leaves no remainder). If so, then is composite. Otherwise, it is prime. [1]
The Mersenne number M 3 = 2 3 −1 = 7 is prime. The Lucas–Lehmer test verifies this as follows. Initially s is set to 4 and then is updated 3−2 = 1 time: s ← ((4 × 4) − 2) mod 7 = 0. Since the final value of s is 0, the conclusion is that M 3 is prime. On the other hand, M 11 = 2047 = 23 × 89 is not prime
Caldwell [10] points out that strong probable prime tests to different bases sometimes provide an additional primality test. Just as the strong test checks for the existence of more than two square roots of 1 modulo n, two such tests can sometimes check for the existence of more than two square roots of −1.
Suppose we wish to determine whether n = 221 is prime.Randomly pick 1 < a < 220, say a = 38.We check the above congruence and find that it holds: = (). Either 221 is prime, or 38 is a Fermat liar, so we take another a, say 24:
AOL latest headlines, entertainment, sports, articles for business, health and world news.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
All Mersenne primes are of the form M p = 2 p − 1, where p is a prime number itself. The smallest Mersenne prime in this table is 2 1398269 − 1. The first column is the rank of the Mersenne prime in the (ordered) sequence of all Mersenne primes; [33] GIMPS has found all known Mersenne primes beginning with the 35th. #
Checkers. The best board game ever, Checkers, is here. Make your move, red or black, and king me! By Masque Publishing