Editing Prime95

{{Short description|Freeware application to search for primes}}
{{Infobox software
| name = Prime95
| logo = Prime95 icon (green).svg
| logo caption = Prime95 icon in its "on" state
| logo size = 32
| screenshot = 
| caption = Prime95 26.5 running on a [[Windows 7]] system
| developer = [[George Woltman]]
| released = {{Start date and age|df=yes|1996|01|03}}
| latest_release_version = 30.19 build 20<ref>{{cite web | url=https://www.mersenne.org/download/ | title=GIMPS - Free Prime95 software downloads - PrimeNet }}</ref>
| latest_release_date = {{start date and age|2024|6|2}}
| latest_preview_version = 30.19 build 21<ref>{{cite web | url=https://download.mersenne.ca/gimps/v30/30.19 | title=Gimps/V30/30.19 - download.mersenne.ca }}</ref>
| latest_preview_date = {{Start date and age|2024|9|14}}
| operating_system = [[Microsoft Windows]], [[macOS]], [[Linux]], [[FreeBSD]]
| programming_language = [[Assembly language|ASM]], [[C (programming language)|C]]
| genre = [[Mersenne prime]] finder / system stability tester
| license = [[Freeware]]<ref name="gimps-legal" />
| website = 
}}
'''Prime95''', also distributed as the command-line utility '''mprime''' for [[FreeBSD]] and [[Linux]], is a [[freeware]] [[application software|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 prime]]s. It is also used in [[overclocking]] to test for system stability.<ref name="auto">{{cite web|url=https://appuals.com/how-to-run-a-cpu-stress-test-using-prime95/|title=How To Run a CPU Stress Test Using Prime95|date=2015-12-10|website=Appuals.com|language=en-US|access-date=2019-05-23}}</ref>

Although most<ref name="3yLvQ">{{cite web|title=The security code or checksum is hard to forge. This is the only source code that is not published.|last=Woltman |first=George|url=https://mersenneforum.org/showpost.php?p=47191&postcount=16}}</ref> of its [[source-available software|source code is available]], Prime95 is not [[free and open-source software]] because its [[end-user license agreement]]<ref name="gimps-legal">{{cite web|url=https://mersenne.org/legal|title=GIMPS Legalese - PrimeNet|website=Great Internet Mersenne Prime Search|access-date=2019-05-08}}</ref> states that if the software is used to find a prime qualifying for a bounty offered by the [[Electronic Frontier Foundation]],<ref name="43mpN">{{cite web|url=https://www.eff.org/awards/coop|title=EFF Cooperative Computing Awards|date=2008-02-29|website=Electronic Frontier Foundation|language=en|access-date=2019-05-08}}</ref> 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<ref>{{cite web|last=Woltman|first=George|date=2021-04-08|title=First time LL is no more|url=https://www.mersenneforum.org/showpost.php?p=575514&postcount=1}}</ref> 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 first checks numbers for trivial [[Composite number|compositeness]] by attempting to find a small [[Factorization|factor]]. As of 2024, test candidates are mainly filtered using [[Pollard's p − 1 algorithm]]. [[Trial division]] is implemented, but Prime95 is rarely used for that work in practice because it can be done much more efficiently using a [[Graphics processing unit|GPU]], due to the type of arithmetic involved. Finally, the [[Lenstra elliptic-curve factorization|elliptic-curve factorization method]] and [[Williams's p + 1 algorithm]] are implemented, but are considered not useful at modern GIMPS testing levels and mostly used in attempts to factor much smaller Mersenne numbers that have already undergone primality testing.

GIMPS has discovered 18 new Mersenne primes since its foundation in 1996, the first 17 of which using Prime95. The 18th and most recent, M<sub>136279841</sub>, was discovered in October 2024 using an [[Nvidia]] GPU, being the first GIMPS discovery to not have used Prime95 and its [[Central processing unit|CPU]] computation.<ref name="tyLOW">{{cite web|url=https://www.mersenne.org/various/history.php|title=GIMPS History - PrimeNet|website=Great Internet Mersenne Prime Search|access-date=2019-05-09}}</ref><ref name="GpuOwl">{{cite web|url=https://github.com/preda/gpuowl|title=GpuOwl - GitHub|website=[[GitHub]] }}</ref><ref name="GIMPS52">{{cite web|url=https://www.mersenne.org/primes/?press=M136279841|title= GIMPS Discovers Largest Known Prime Number:2<sup>136,279,841</sup>-1}}</ref> 15 of the 17 primes discovered with Prime95 were the [[largest known prime number]] at the time of their respective discoveries, the exceptions being M<sub>37156667</sub> and M<sub>42643801</sub>, which were discovered out of order from the larger M<sub>43112609</sub>.<ref>{{cite web|title=GIMPS Milestones|url=https://www.mersenne.org/report_milestones/|access-date=2021-10-17|website=www.mersenne.org}}</ref>

== Use for stress testing ==

[[File:Prime95 28.7 quad-core.png|thumb|250px|Prime95 28.7 running a stress test on an [[Intel]] quad-core [[Windows 10]] system]]

To maximize search throughput, most of Prime95 is written in hand-tuned [[Assembly language|assembly]], 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 [[Overclocking|overclockers]] to check the stability of a particular configuration.<ref name="auto" />

== See also ==
* [[List of volunteer computing projects]]
* [[Torture testing|Stress testing]]
* [[Prime number]]
* [[PrimeGrid]]

==References==
{{reflist|1=30em}}

==External links==
* {{official website}} with downloads for various architectures
* How to use Prime95 for stress (torture) testing<ref>{{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}}</ref>

[[Category:Volunteer computing projects]]
[[Category:Primality tests]]
[[Category:Benchmarks (computing)]]
[[Category:Great Internet Mersenne Prime Search]]
[[Category:Science software for macOS]]
[[Category:Science software for Windows]]
[[Category:Science software for Linux]]
[[Category:BSD software]]
[[Category:Mathematical software]]