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In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form N = k ⋅ 2 n − 1 with odd k < 2 n. The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form.
The Lucas-Lehmer residue calculated with these alternative starting values will still be zero if M p is a Mersenne prime. However, the terms of the sequence will be different and a non-zero Lucas-Lehmer residue for non-prime M p will have a different numerical value from the non-zero value calculated when s 0 = 4.
Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991), almost always cited as D.H. Lehmer, [1] [2] [3] was an American mathematician significant to the development of computational number theory. Lehmer refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes.
In computational number theory, the Lucas test is a primality test for a natural number n; it requires that the prime factors of n − 1 be already known. [ 1 ] [ 2 ] It is the basis of the Pratt certificate that gives a concise verification that n is prime.
Different subprojects may run on different operating systems, and may have executables for CPUs, GPUs, or both; while running the Lucas–Lehmer–Riesel test, CPUs with Advanced Vector Extensions and Fused Multiply-Add instruction sets will yield the fastest results for non-GPU accelerated workloads.
Lucas Primality Test with Factored N − 1 (MathPages.com) at the Library of Congress Web Archives (archived 2010-08-06) PRIMABOINCA is a research project that uses Internet-connected computers to search for a counterexample to some conjectures.
Riesel also discovered the Riesel numbers as well as developing the Lucas–Lehmer–Riesel test. After having worked at the Swedish Board for Computing Machinery , he was awarded his Ph.D. from Stockholm University in 1969 for his thesis Contributions to numerical number theory , [ 4 ] [ 5 ] and in the same year joined the Royal Institute of ...
Lucas–Lehmer primality test; Lucas–Lehmer–Riesel test; M. Miller–Rabin primality test; MPrime; P. Pépin's test; Perrin number; Pocklington primality test ...