Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a

freeware Freeware is software, most often proprietary, that is distributed at no monetary cost to the end user. There is no agreed-upon set of rights, license, or EULA that defines ''freeware'' unambiguously; every publisher defines its own rules for the ...

application written by

George Woltman 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 Institu ...

. 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 In computing, overclocking is the practice of increasing the clock rate of a computer to exceed that certified by the manufacturer. Commonly, operating voltage is also increased to maintain a component's operational stability at accelerated spe ...

to test for system stability. Although most of its source code is available, Prime95 is not free and open-source software because its end-user license agreement states that if the software is used to find a prime qualifying for a bounty offered by the Electronic Frontier Foundation, then that bounty will be claimed and distributed by GIMPS.

Finding Mersenne primes by volunteer computing

Prime95 tests numbers for primality using the Fermat primality test (referred to internally as PRP, or "probable prime"). For much of its history, it used the Lucas–Lehmer primality test, but the availability of Lucas–Lehmer assignments was deprecated in April 2021 to increase search throughput. Specifically, to guard against faulty results, every Lucas–Lehmer test had to be performed twice in its entirety, while Fermat tests can be verified in a small fraction of their original run time using a proof generated during the test by Prime95. Current versions of Prime95 remain capable of Lucas–Lehmer testing for the purpose of double-checking existing Lucas–Lehmer results, and for fully verifying "probably prime" Fermat test results (which, unlike "prime" Lucas–Lehmer results, are not conclusive). To reduce the number of full-length primality tests needed, Prime95 also implements other, computationally simpler tests designed to filter out unviable candidates; as of 2021, this mainly comprises Pollard's p – 1 algorithm. The elliptic-curve factorization method and (in preview releases starting with 30.6) Williams's p + 1 algorithm are implemented, but are considered not useful at modern GIMPS testing levels, and mostly used in attempts to

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much smaller Mersenne numbers that have already undergone primality testing. Prime95 implements

trial division Trial division is the most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests to see if an integer ''n'', the integer to be factored, can be divided by each number in turn t ...

, but because this type of work can be executed using

single-precision Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating- ...

arithmetic (as opposed to the

double-precision Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Flo ...

arithmetic required by other GIMPS work types), almost all GIMPS trial division is done by third-party clients implementing GPU computation for its comparatively much greater single-precision throughput. GIMPS has discovered 17 new Mersenne primes since its foundation in 1996, all using Prime95. Each was the largest known prime number at the time of its discovery, except M_37156667 and M_42643801, which were discovered out of order from the larger M_43112609.

Use for stress testing

To maximize search throughput, most of Prime95 is written in hand-tuned

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, which makes its system resource usage much greater than most other computer programs. Additionally, due to the high precision requirements of primality testing, the program is very sensitive to computation errors and proactively reports them. These factors make it a commonly used tool among

overclockers In computing, overclocking is the practice of increasing the clock rate of a computer to exceed that certified by the manufacturer. Commonly, operating voltage is also increased to maintain a component's operational stability at accelerated spe ...

to check the stability of a particular configuration.

References

External links

* with downloads for various architectures * How to use Prime95 for stress (torture) testing{{Cite web , title=Torture test your CPU with Prime95 , url=http://www.playtool.com/pages/prime95/prime95.html , access-date=2022-09-15 , website=www.playtool.com Volunteer computing projects Primality tests Benchmarks (computing) Great Internet Mersenne Prime Search Science software for macOS Science software for Windows Science software for Linux BSD software Mathematical software

Finding Mersenne primes by volunteer computing

Use for stress testing

See also

References

External links