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Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in overclocking to test for system ...
The proof files are generated while the Fermat primality test is in progress. These proofs, together with an error-checking algorithm devised by Robert Gerbicz, provide a complete confidence in the correctness of the test result and eliminate the need for double checks. First-time Lucas-Lehmer tests were deprecated in April 2021. [15]
George Woltman (born November 10, 1957) is the founder of the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project researching Mersenne prime numbers using his software Prime95. He graduated from the Massachusetts Institute of Technology (MIT) with a degree in computer science. He lives in North Carolina.
The idea beneath this test is that when n is an odd prime, it passes the test because of two facts: by Fermat's little theorem , a n − 1 ≡ 1 ( mod n ) {\displaystyle a^{n-1}\equiv 1{\pmod {n}}} (this property alone defines the weaker notion of probable prime to base a , on which the Fermat test is based);
For constant k, this is in the same complexity class as the Lucas-Lehmer test, and is similarly fast in practice. The most efficient deterministic primality test for any n-digit number, the AKS primality test, requires Õ(n 6) bit operations in its best known variant and is extremely slow even for relatively small values.
The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian Institute of Technology Kanpur, on August 6, 2002, in an article titled "PRIMES is in P". [1]
64 31×2 15145093 – 1 9 February 2025 4,559,129 65 69×2 14977631 – 1 3 December 2021 4,508,719 66 192971×2 14773498 – 1 7 March 2021 4,447,272 67 4×3 9214845 + 1 10 September 2024 4,396,600 68 9145334×3 9145334 + 1 25 December 2023 4,363,441 69 4×5 6181673 – 1 15 July 2022 4,320,805 70 396101×2 14259638 – 1 3 February 2024 ...
An alternative program for this would be Prime95. The advantage of the program lies in the fact that (partial) calculations can be carried out on an old Pentium PC, an up-to-date workstation , and theoretically even supercomputers , without measured performance falling off a measurement scale (or complex benchmarks becoming incompatible due to ...