Prime95, also distributed as the command-line utility mprime for

FreeBSD FreeBSD is a free and open-source Unix-like operating system descended from the Berkeley Software Distribution (BSD), which was based on Research Unix. The first version of FreeBSD was released in 1993. In 2005, FreeBSD was the most popular ...

and

Linux Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which i ...

, 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 t ...

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 The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. GIMPS was founded in 1996 by George Woltman, who also wrote the Prime95 client an ...

(GIMPS), a

volunteer computing Volunteer computing is a type of distributed computing in which people donate their computers' unused resources to a research-oriented project, and sometimes in exchange for credit points. The fundamental idea behind it is that a modern desktop co ...

project dedicated to searching for

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...

s. 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 Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source ...

because its

end-user license agreement An end-user license agreement or EULA () is a legal contract between a software Software is a set of computer programs and associated software documentation, documentation and data (computing), data. This is in contrast to Computer hardware ...

states that if the software is used to find a prime qualifying for a bounty offered by the

Electronic Frontier Foundation The Electronic Frontier Foundation (EFF) is an international non-profit digital rights group based in San Francisco, California. The foundation was formed on 10 July 1990 by John Gilmore, John Perry Barlow and Mitch Kapor to promote Internet ...

, 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 The Fermat primality test is a probabilistic test to determine whether a number is a probable prime. Concept Fermat's little theorem states that if ''p'' is prime and ''a'' is not divisible by ''p'', then :a^ \equiv 1 \pmod. If one wants to tes ...

(referred to internally as PRP, or "probable prime"). For much of its history, it used the

Lucas–Lehmer primality test In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1876 and subsequently improved by Derrick Henry Lehmer in the 1930s. The test The Lucas–Lehmer t ...

, 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

factor Factor, a Latin word meaning "who/which acts", may refer to: Commerce * Factor (agent), a person who acts for, notably a mercantile and colonial agent * Factor (Scotland), a person or firm managing a Scottish estate * Factors of production, ...

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 ...

, 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 floati ...

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. Fl ...

arithmetic required by other GIMPS work types), almost all GIMPS trial division is done by third-party clients implementing

GPU A graphics processing unit (GPU) is a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device. GPUs are used in embedded systems, mob ...

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 The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A prime number is a pos ...

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

assembly Assembly may refer to: Organisations and meetings * Deliberative assembly, a gathering of members who use parliamentary procedure for making decisions * General assembly, an official meeting of the members of an organization or of their representa ...

, 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 ...

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