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Baillie–PSW Primality Test
The Baillie–PSW primality test is a probabilistic primality testing algorithm that determines whether a number is composite or is a probable prime. It is named after Robert Baillie, Carl Pomerance, John Selfridge, and Samuel Wagstaff. The Baillie–PSW test is a combination of a strong Fermat probable prime test to base 2 and a strong Lucas probable prime test. The Fermat and Lucas test each have their own list of pseudoprimes, that is, composite numbers that pass the test. For example, the first ten strong pseudoprimes to base 2 are : 2047, 3277, 4033, 4681, 8321, 15841, 29341, 42799, 49141, and 52633 . The first ten strong Lucas pseudoprimes (with Lucas parameters (''P'', ''Q'') defined by Selfridge's Method A) are : 5459, 5777, 10877, 16109, 18971, 22499, 24569, 25199, 40309, and 58519 . There is no known overlap between these lists of strong Fermat pseudoprimes and strong Lucas pseudoprimes, and there is even evidence that the numbers in these lists tend to be different kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized algor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
