https://www.rieselprime.de/z/api.php?action=feedcontributions&user=GeekPrime&feedformat=atomPrime-Wiki - User contributions [en]2024-03-29T14:18:18ZUser contributionsMediaWiki 1.31.1https://www.rieselprime.de/z/index.php?title=Prime95&diff=12579Prime952020-12-03T18:14:09Z<p>GeekPrime: /* Implementation */</p>
<hr />
<div>{{InfoboxProgram|title=Prime95 / Mprime|workload=[[Lucas-Lehmer test|LL]], PRP, [[Trial factoring|TF]], [[P-1 factorization method|P-1]], [[Elliptic curve method|ECM]]|release=1996|latest=30.3b6<br/><small>2020-09-11</small>}}<br />
'''Prime95''' is the freeware computer program written by [[George Woltman]] that is used by [[Great Internet Mersenne Prime Search|GIMPS]], a [[distributed computing]] project dedicated to finding new [[Mersenne prime]] numbers. More specifically, Prime95 refers to the Windows and Mac OS X versions of the software.<br />
<br />
'''MPrime''' is the [[Linux]] command-line interface version of Prime95, to be run in a text terminal or in a terminal emulator window as a remote shell client. It is identical to Prime95 in functionality, except it lacks a graphical user interface.<br />
<br />
As of December 2018, Prime95 was used to discover all 17 Mersenne primes found by GIMPS.<br />
<br />
==Implementation==<br />
Although most of the GIMPS software's source code is publicly available, it is technically not free software as users must abide by the project's distribution [http://www.mersenne.org/legal/ terms] if the software is used to discover a prime number with at least {{Num|100000000}} decimal digits and wins the ${{Num|150000}} bounty offered by the [[Electronic Frontier Foundation|EFF]] ([https://www.eff.org/awards/coop Cooperative Computing Awards]). As such, a user who uses Prime95 to discover a qualifying prime number would not be able to claim the prize directly. A free software package would not have this restriction.<br />
<br />
The code that is used to generate checksums is not publicly available due to [http://mersenneforum.org/showpost.php?p=47191&postcount=16 security reasons]. The rewritten FFT assembly code in the versions since 27 (May 2012) uses [[Advanced Vector Extensions|AVX]] instructions of Intel's Sandy Bridge and Ivy Bridge CPUs (Core i3/i5/i7-2xxx and 3xxx models), resulting in a huge performance increase compared to previous versions.<br />
<br />
Prime95 currently does not have [[GPU]] support, although Woltman has indicated that it is under development. However, there are third-party programs, such as [[CUDALucas]], [[gpuOwL]] and [[clLucas]], that make use of the processing power of GPUs.<br />
<br />
Before version 30 of Prime95, primality testing relied on double-checking of the results by running the primality tests twice or more times (if the recorded checksums did not match on GIMPS server). Version 30 instead relies on a [https://eprint.iacr.org/2018/627.pdf breakthrough] by [[Krzysztof Pietrzak]], which allows to produce a proof file that can be securely verified with less than 0.5% of the work required to re-run the primality test.<br />
<br />
==Finding Mersenne primes by distributed computing==<br />
[http://primes.utm.edu/bios/page.php?id=42 As of December 2018], 17 new [[Mersenne prime]]s have been found by the network of participants, and, on average, a new Mersenne prime is discovered approximately every year. [[Scott Kurowski]] wrote the Internet [[PrimeNet]] server that supports the Prime95/MPrime software on [[GIMPS]], one of the earliest [[grid computing]] projects, researching Mersenne prime numbers, to demonstrate distributed computing software of Entropia, a company he founded in 1997.<br />
<br />
===Processing power===<br />
A table of selected benchmarks is provided below. The complete list can be found at the official GIMPS website.<br />
<br />
{| style="font-size: 85%; text-align: center" border="1" style="border: 1px solid #afafaf; background-color: #f9f9f9; border-collapse: collapse;" cellpadding="2"<br />
|-<br />
!Comparison of CPU core power!!Frequency!!Cores!!colspan="2" | [[Fast Fourier transform|FFT]]!![[Trial factoring]]!!TDP<br />
|-<br />
![http://www.mersenne.org/report_benchmarks/ Prime95 benchmark]!!(per core)!! !!2048k!!4096k!!65-bit!!<br />
|-<br />
!Platform [[CPU]] model!!MHz!! !!ms!!ms!!ms!!Watts<br />
|-<br />
|style="text-align:left"|Intel Atom 330||1600||2||621||1166||46||8<br />
|-<br />
|style="text-align:left"|Intel Atom D510||1664||2||585.91||1954.40||25.65||13<br />
|-<br />
|style="text-align:left"|Intel Pentium III||1151||1||438.10||922.58||50.59||30<br />
|-<br />
|style="text-align:left"|AMD Athlon||1054||1||457.40||774.49||56.08||?<br />
|-<br />
|style="text-align:left"|AMD Fusion E-350||1596||2||222.03||491.02||15.18||18<br />
|-<br />
|style="text-align:left"|AMD Athlon XP 2000+||1640||1||201.21||448.28||32.80||~60<br />
|-<br />
|style="text-align:left"|Intel Pentium 4||3078||1||72.40||162.02||14.91||86<br />
|-<br />
|style="text-align:left"|AMD Phenom II X4||3414||4||34.86||76.27||4.59||125<br />
|-<br />
|style="text-align:left"|Intel Core2 Duo E8600||3334||2||34.15||73.07||4.89||65<br />
|-<br />
|style="text-align:left\"|Sandy Bridge Pentium G620T||2159||2||41.09||72.53||4.99||35<br />
|-<br />
|style="text-align:left"|AMD Phenom II X6 1100T||3310||6||32.68||69.54||3.85||125<br />
|-<br />
|style="text-align:left"|Intel Core i5-2500K||3330||4||23.94||53.24||3.49||95<br />
|-<br />
|style="text-align:left"|Intel Core i7-2600K||3463||4||21.75||45.35||3.67||95<br />
|}<br />
<br />
==Use for stress testing==<br />
Over the years, Prime95 has become extremely popular among [[Personal computer|PC]] enthusiasts and [[Overclocking|overclockers]] as a stability testing utility. It includes a "Torture Test" mode designed specifically for testing PC subsystems for errors in order to help ensure the correct operation of Prime95 on that system. This is important because each iteration of the Lucas-Lehmer depends on the previous one; if one iteration is incorrect, so will be the entire primality test.<br />
<br />
The stress-test feature in Prime95 can be configured to better test various components of the computer by changing the [[Fast Fourier transform]] (FFT) size. Three pre-set configurations are available: Small FFTs and In-place FFTs, and Blend. Small and In-place modes primarily test the FPU and the caches of the CPU, whereas the Blend mode tests everything, including the memory.<br />
<br />
By selecting Custom, the user can gain further control of the configuration. For example, by selecting 8-8 kB as the FFT size, the program stresses primarily the CPU. By selecting 2048-4096 kB and unchecking the "Run FFTs in-place" checkbox, providing the maximum amount of RAM free in the system, the program tests the memory and the chipset. If the amount of memory to use option is set too high, then the system will start using the paging file and the test will not stress the memory.<br />
<br />
On an absolutely stable system, Prime95 would run indefinitely. If an error occurs, at which point the stress test would terminate, this would indicate that the system may be unstable. There is an ongoing debate about terms "stable" and "Prime-stable", as Prime95 often fails before the system becomes unstable or crashes in any other application. This is because Prime95 is ''designed'' to subject the CPU to an incredibly intense workload, and to halt when it encounters even one minor error, whereas most normal applications do not stress the CPU anywhere near as much, and will continue to operate unless they encounter a fatal error.<br />
<br />
In the overclocking community, a rule of thumb is often used to determine how long to run Prime95: test the CPU (8 kB FFT) for 10 hours and the memory (4096 kB FFT) for 10 hours, and if the system passes, there is a high chance that it is stable. Twenty-four hours of testing is recommended to be sure, as errors may show up after 16 or more hours of testing (compared to, say, just four hours of testing).<br />
<!-- The ref source page recommends 24 hours testing non-stop http://www.ocforums.com/showthread.php?t=335813 (no available/moved)--><br />
Moreover, a large proportion of system [[Overclocking|overclockers]] and enthusiasts favor Prime95 over other benchmarking suites because Prime95 pushes the CPU's floating point units extremely hard, causing the CPU to become extremely hot. In addition, Prime95 stresses a computer far more than the majority of software based torture-suites. The nature of this is because the operating system usually shuts down the floating-point unit when unused by other programs, whereas Prime95 is well-optimized to continuously and effectively thread the FPU, causing it to be deeply pipelined, thereby generating significantly more heat because of elevated power consumption under the massive workload conditions. In CPUs which are not adequately cooled, errors are likely to occur. Prime95 also constantly accesses main memory at up to 60 MB per second. This constant activity will detect memory problems that other programs will not.<br />
<br />
Lastly, power supply units of any machine running Prime95 are subject to the consistent ramifications of such harsh conditions. Power must be maintained clean, while providing adequate voltage, particularly to the CPU, RAM, and chipsets (mainboard chipsets such as the Northbridge where the memory controller may or may not reside; see Athlon 64 or Intel Core i7 for on-die memory controllers) to provide peak performance while maintaining stability. [[Cray Research]] used programs similar to Prime95 for over a decade for the purpose of [http://www.xs4all.nl/~mfvl/prime/readme.txt stability testing].<br />
<br />
==Limits==<br />
Version 24 and older of Prime95 cannot test Mersenne numbers beyond 2<sup>{{Num|79300000}}</sup>-1 ([http://web.archive.org/web/20080606075920/http://www.starqwest.org/page4.html Web Archive]). This is slightly shorter than a 24 million digit number. Newer versions of Prime95 (version 25, 26 and 27) can handle Mersenne numbers up to the limit 2<sup>{{Num|596000000}}</sup>-1 ([http://www.mersenneforum.org/showthread.php?p=258001&highlight=596000000#post258001 see here]).<br />
<br />
Prime95 does not fully stress all processor threads when the threads number is more than 64 in Windows, or 32 for the 32-bit version. Windows will manage the processors in groups when the number beyond 64. Each group will only have maximum of 64. Prime95 will only load into one processor group.<br />
<br />
==Prime 95 and MPrime Release history==<br />
{{Changelog/Prime95}}<br />
<br />
==Worktodo.txt==<br />
:''Main article:'' [[worktodo.txt]]<br />
:File <code>worktodo.txt</code> takes Lucas-Lehmer test assignments in the following formats:[http://mersenneforum.org/mayer/README.html]<br />
<br />
<nowiki>Test=<ASSIGNMENT ID>,<EXPONENT>,<TRIAL FACTORING EXPONENT>,<P-1 FACTORING></nowiki><br />
<nowiki>DoubleCheck=<ASSIGNMENT ID>,<EXPONENT>,<TRIAL FACTORING EXPONENT>,<P-1 FACTORING></nowiki><br />
<br />
Where:<br />
*<code><ASSIGNMENT ID></code> - unique assignment ID generated by the PrimeNet v5 server as an anti-poaching measure<br />
*<code><EXPONENT></code> - Mersenne number exponent<br />
*<code><TRIAL FACTORING EXPONENT></code> - indicates power of 2 to which trial factoring had been attempted<br />
*<code><nowiki><P-1 FACTORING></nowiki></code>:<br />
**0 indicates that p-1 factoring still needs to be done<br />
**1 indicates that p-1 factoring attempted with no small factors found<br />
<br />
Examples:<br />
<br />
Test=DDD21F2A0B252E499A9F9020E02FE232,48295213,69,0<br />
DoubleCheck=B83D23BF447184F586470457AD1E03AF,22831811,66,1<br />
<br />
==See also==<br />
*[[GIMPS clients]]<br />
*[[Mlucas]]<br />
*[[Glucas]]<br />
*[[GPU#GPU_clients|GPU clients]]<br />
*[[Primality testing program]]<br />
<br />
==External links==<br />
*[https://www.mersenne.org/download/ Prime95 download page]<br />
[[Category:Software]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Prime95&diff=12578Prime952020-12-03T18:07:08Z<p>GeekPrime: new version</p>
<hr />
<div>{{InfoboxProgram|title=Prime95 / Mprime|workload=[[Lucas-Lehmer test|LL]], PRP, [[Trial factoring|TF]], [[P-1 factorization method|P-1]], [[Elliptic curve method|ECM]]|release=1996|latest=30.3b6<br/><small>2020-09-11</small>}}<br />
'''Prime95''' is the freeware computer program written by [[George Woltman]] that is used by [[Great Internet Mersenne Prime Search|GIMPS]], a [[distributed computing]] project dedicated to finding new [[Mersenne prime]] numbers. More specifically, Prime95 refers to the Windows and Mac OS X versions of the software.<br />
<br />
'''MPrime''' is the [[Linux]] command-line interface version of Prime95, to be run in a text terminal or in a terminal emulator window as a remote shell client. It is identical to Prime95 in functionality, except it lacks a graphical user interface.<br />
<br />
As of December 2018, Prime95 was used to discover all 17 Mersenne primes found by GIMPS.<br />
<br />
==Implementation==<br />
Although most of the GIMPS software's source code is publicly available, it is technically not free software as users must abide by the project's distribution [http://www.mersenne.org/legal/ terms] if the software is used to discover a prime number with at least {{Num|100000000}} decimal digits and wins the ${{Num|150000}} bounty offered by the [[Electronic Frontier Foundation|EFF]] ([https://www.eff.org/awards/coop Cooperative Computing Awards]). As such, a user who uses Prime95 to discover a qualifying prime number would not be able to claim the prize directly. A free software package would not have this restriction.<br />
<br />
The code that is used to generate checksums is not publicly available due to [http://mersenneforum.org/showpost.php?p=47191&postcount=16 security reasons]. The rewritten FFT assembly code in the versions since 27 (May 2012) uses [[Advanced Vector Extensions|AVX]] instructions of Intel's Sandy Bridge and Ivy Bridge CPUs (Core i3/i5/i7-2xxx and 3xxx models), resulting in a huge performance increase compared to previous versions.<br />
<br />
Prime95 currently does not have [[GPU]] support, although Woltman has indicated that it is under development. However, there are third-party programs, such as [[CUDALucas]], [[gpuOwL]] and [[clLucas]], that make use of the processing power of GPUs.<br />
<br />
==Finding Mersenne primes by distributed computing==<br />
[http://primes.utm.edu/bios/page.php?id=42 As of December 2018], 17 new [[Mersenne prime]]s have been found by the network of participants, and, on average, a new Mersenne prime is discovered approximately every year. [[Scott Kurowski]] wrote the Internet [[PrimeNet]] server that supports the Prime95/MPrime software on [[GIMPS]], one of the earliest [[grid computing]] projects, researching Mersenne prime numbers, to demonstrate distributed computing software of Entropia, a company he founded in 1997.<br />
<br />
===Processing power===<br />
A table of selected benchmarks is provided below. The complete list can be found at the official GIMPS website.<br />
<br />
{| style="font-size: 85%; text-align: center" border="1" style="border: 1px solid #afafaf; background-color: #f9f9f9; border-collapse: collapse;" cellpadding="2"<br />
|-<br />
!Comparison of CPU core power!!Frequency!!Cores!!colspan="2" | [[Fast Fourier transform|FFT]]!![[Trial factoring]]!!TDP<br />
|-<br />
![http://www.mersenne.org/report_benchmarks/ Prime95 benchmark]!!(per core)!! !!2048k!!4096k!!65-bit!!<br />
|-<br />
!Platform [[CPU]] model!!MHz!! !!ms!!ms!!ms!!Watts<br />
|-<br />
|style="text-align:left"|Intel Atom 330||1600||2||621||1166||46||8<br />
|-<br />
|style="text-align:left"|Intel Atom D510||1664||2||585.91||1954.40||25.65||13<br />
|-<br />
|style="text-align:left"|Intel Pentium III||1151||1||438.10||922.58||50.59||30<br />
|-<br />
|style="text-align:left"|AMD Athlon||1054||1||457.40||774.49||56.08||?<br />
|-<br />
|style="text-align:left"|AMD Fusion E-350||1596||2||222.03||491.02||15.18||18<br />
|-<br />
|style="text-align:left"|AMD Athlon XP 2000+||1640||1||201.21||448.28||32.80||~60<br />
|-<br />
|style="text-align:left"|Intel Pentium 4||3078||1||72.40||162.02||14.91||86<br />
|-<br />
|style="text-align:left"|AMD Phenom II X4||3414||4||34.86||76.27||4.59||125<br />
|-<br />
|style="text-align:left"|Intel Core2 Duo E8600||3334||2||34.15||73.07||4.89||65<br />
|-<br />
|style="text-align:left\"|Sandy Bridge Pentium G620T||2159||2||41.09||72.53||4.99||35<br />
|-<br />
|style="text-align:left"|AMD Phenom II X6 1100T||3310||6||32.68||69.54||3.85||125<br />
|-<br />
|style="text-align:left"|Intel Core i5-2500K||3330||4||23.94||53.24||3.49||95<br />
|-<br />
|style="text-align:left"|Intel Core i7-2600K||3463||4||21.75||45.35||3.67||95<br />
|}<br />
<br />
==Use for stress testing==<br />
Over the years, Prime95 has become extremely popular among [[Personal computer|PC]] enthusiasts and [[Overclocking|overclockers]] as a stability testing utility. It includes a "Torture Test" mode designed specifically for testing PC subsystems for errors in order to help ensure the correct operation of Prime95 on that system. This is important because each iteration of the Lucas-Lehmer depends on the previous one; if one iteration is incorrect, so will be the entire primality test.<br />
<br />
The stress-test feature in Prime95 can be configured to better test various components of the computer by changing the [[Fast Fourier transform]] (FFT) size. Three pre-set configurations are available: Small FFTs and In-place FFTs, and Blend. Small and In-place modes primarily test the FPU and the caches of the CPU, whereas the Blend mode tests everything, including the memory.<br />
<br />
By selecting Custom, the user can gain further control of the configuration. For example, by selecting 8-8 kB as the FFT size, the program stresses primarily the CPU. By selecting 2048-4096 kB and unchecking the "Run FFTs in-place" checkbox, providing the maximum amount of RAM free in the system, the program tests the memory and the chipset. If the amount of memory to use option is set too high, then the system will start using the paging file and the test will not stress the memory.<br />
<br />
On an absolutely stable system, Prime95 would run indefinitely. If an error occurs, at which point the stress test would terminate, this would indicate that the system may be unstable. There is an ongoing debate about terms "stable" and "Prime-stable", as Prime95 often fails before the system becomes unstable or crashes in any other application. This is because Prime95 is ''designed'' to subject the CPU to an incredibly intense workload, and to halt when it encounters even one minor error, whereas most normal applications do not stress the CPU anywhere near as much, and will continue to operate unless they encounter a fatal error.<br />
<br />
In the overclocking community, a rule of thumb is often used to determine how long to run Prime95: test the CPU (8 kB FFT) for 10 hours and the memory (4096 kB FFT) for 10 hours, and if the system passes, there is a high chance that it is stable. Twenty-four hours of testing is recommended to be sure, as errors may show up after 16 or more hours of testing (compared to, say, just four hours of testing).<br />
<!-- The ref source page recommends 24 hours testing non-stop http://www.ocforums.com/showthread.php?t=335813 (no available/moved)--><br />
Moreover, a large proportion of system [[Overclocking|overclockers]] and enthusiasts favor Prime95 over other benchmarking suites because Prime95 pushes the CPU's floating point units extremely hard, causing the CPU to become extremely hot. In addition, Prime95 stresses a computer far more than the majority of software based torture-suites. The nature of this is because the operating system usually shuts down the floating-point unit when unused by other programs, whereas Prime95 is well-optimized to continuously and effectively thread the FPU, causing it to be deeply pipelined, thereby generating significantly more heat because of elevated power consumption under the massive workload conditions. In CPUs which are not adequately cooled, errors are likely to occur. Prime95 also constantly accesses main memory at up to 60 MB per second. This constant activity will detect memory problems that other programs will not.<br />
<br />
Lastly, power supply units of any machine running Prime95 are subject to the consistent ramifications of such harsh conditions. Power must be maintained clean, while providing adequate voltage, particularly to the CPU, RAM, and chipsets (mainboard chipsets such as the Northbridge where the memory controller may or may not reside; see Athlon 64 or Intel Core i7 for on-die memory controllers) to provide peak performance while maintaining stability. [[Cray Research]] used programs similar to Prime95 for over a decade for the purpose of [http://www.xs4all.nl/~mfvl/prime/readme.txt stability testing].<br />
<br />
==Limits==<br />
Version 24 and older of Prime95 cannot test Mersenne numbers beyond 2<sup>{{Num|79300000}}</sup>-1 ([http://web.archive.org/web/20080606075920/http://www.starqwest.org/page4.html Web Archive]). This is slightly shorter than a 24 million digit number. Newer versions of Prime95 (version 25, 26 and 27) can handle Mersenne numbers up to the limit 2<sup>{{Num|596000000}}</sup>-1 ([http://www.mersenneforum.org/showthread.php?p=258001&highlight=596000000#post258001 see here]).<br />
<br />
Prime95 does not fully stress all processor threads when the threads number is more than 64 in Windows, or 32 for the 32-bit version. Windows will manage the processors in groups when the number beyond 64. Each group will only have maximum of 64. Prime95 will only load into one processor group.<br />
<br />
==Prime 95 and MPrime Release history==<br />
{{Changelog/Prime95}}<br />
<br />
==Worktodo.txt==<br />
:''Main article:'' [[worktodo.txt]]<br />
:File <code>worktodo.txt</code> takes Lucas-Lehmer test assignments in the following formats:[http://mersenneforum.org/mayer/README.html]<br />
<br />
<nowiki>Test=<ASSIGNMENT ID>,<EXPONENT>,<TRIAL FACTORING EXPONENT>,<P-1 FACTORING></nowiki><br />
<nowiki>DoubleCheck=<ASSIGNMENT ID>,<EXPONENT>,<TRIAL FACTORING EXPONENT>,<P-1 FACTORING></nowiki><br />
<br />
Where:<br />
*<code><ASSIGNMENT ID></code> - unique assignment ID generated by the PrimeNet v5 server as an anti-poaching measure<br />
*<code><EXPONENT></code> - Mersenne number exponent<br />
*<code><TRIAL FACTORING EXPONENT></code> - indicates power of 2 to which trial factoring had been attempted<br />
*<code><nowiki><P-1 FACTORING></nowiki></code>:<br />
**0 indicates that p-1 factoring still needs to be done<br />
**1 indicates that p-1 factoring attempted with no small factors found<br />
<br />
Examples:<br />
<br />
Test=DDD21F2A0B252E499A9F9020E02FE232,48295213,69,0<br />
DoubleCheck=B83D23BF447184F586470457AD1E03AF,22831811,66,1<br />
<br />
==See also==<br />
*[[GIMPS clients]]<br />
*[[Mlucas]]<br />
*[[Glucas]]<br />
*[[GPU#GPU_clients|GPU clients]]<br />
*[[Primality testing program]]<br />
<br />
==External links==<br />
*[https://www.mersenne.org/download/ Prime95 download page]<br />
[[Category:Software]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=MediaWiki_talk:Sitenotice&diff=8073MediaWiki talk:Sitenotice2020-06-05T16:08:38Z<p>GeekPrime: Created page with "This site notice is too intrusive and irrelevant to many visitors. Also, some articles still display the notice from April. --~~~~"</p>
<hr />
<div>This site notice is too intrusive and irrelevant to many visitors.<br />
<br />
Also, some articles still display the notice from April. --[[User:GeekPrime|GeekPrime]] ([[User talk:GeekPrime|talk]]) 16:08, 5 June 2020 (UTC)</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=ECPP-DJ&diff=6009ECPP-DJ2019-12-02T18:04:56Z<p>GeekPrime: </p>
<hr />
<div>{{InfoboxProgram<br />
|title=ECPP-DJ<br />
|workload=ECPP, [[BLS75]],<br>BPSW, AKS<br />
|release=2013<br />
|latest=1.04<br><small>2014-08-16</small><br />
}}<br />
'''ECPP-DJ''' is a primality testing program created by [[Dana Jacobsen]].<br />
<br />
It is written in C using the GMP library. It is a standalone version of the ECPP implementation written for the Perlmodule '''M'''ath::'''P'''rime::'''U'''til::GMP ('''MPU''') in 2013.<br />
<br />
It implements the following algorithms:<br />
*[[ECPP test]]<br />
*[[BPSW test]] (strong PRP-2 test followed by extra strong Lucas-Selfridge test)<br />
*[[AKS test]]<br />
*[[BLS75]] (particularly, theorems 5/7 and 19)<br />
<br />
Most of the utility functions closely follow the algorithms presented in Henri Cohen's book [http://plouffe.fr/simon/math/A%20course%20in%20computational%20algebraic%20number%20theory%20-%20Cohen.pdf "A Course in Computational Algebraic Number Theory"] (1993). The ECM factoring and manipulation was heavily inspired by [[GMP-ECM]] by [[Paul Zimmermann]] and many others.<br />
<br />
It can verify ECPP certificates, which were generated by this program (or MPU) as well as [[Primo]]. It can be linked with [[MPZ APR-CL]] code to enable the [[Adleman–Pomerance–Rumely primality test|APR-CL]] test.<br />
<br />
Unlike Primo, this is an open-source implementation of ECPP test. However, Primo runs much faster for 1000+ digit numbers, especially on multi-core machines (ECPP-DJ is single threaded).<br />
<br />
==Example usage==<br />
To verify [[M12]] using BLS75:<br />
:$./ecpp-dj -V -bls 170141183460469231731687303715884105727<br />
:N: 170141183460469231731687303715884105727<br />
:BLS75 proof using N-1<br />
:PRIME<br />
<br />
==External links==<br />
*[https://github.com/danaj/Math-Prime-Util-GMP Math::Prime::Util::GMP] at GitHub<br />
*[http://www.mersenneforum.org/showthread.php?t=18283 ECPP-DJ thread] at [[MersenneForum]]<br />
[[Category:Software]]<br />
[[Category:Primality testing program]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=GMP-ECM&diff=6008GMP-ECM2019-12-02T18:03:40Z<p>GeekPrime: </p>
<hr />
<div>'''GMP-ECM''' is a program capable of factoring numbers using the [[Elliptic curve method|ECM]], [[P-1 factorization method|p-1]] and [[P+1 factorization method|p+1]] algorithms. The current version is 7.0.5-dev (svn 3038).<br />
<br />
Originally developed by [[Paul Zimmermann]]. He was joined by Alexander Kruppa at release 5. Currently the program is developed by a team of contributors.<ref>[https://gforge.inria.fr/project/memberlist.php?group_id=135 Project Member List] – InriaForge: GMP-ECM.</ref><br />
<br />
Distributed under GNU General Public License version 2.<br />
<br />
==Compiling GMP-ECM on Windows==<br />
To get an optimal performance, you'll need to compile (build) your own version of GMP-ECM.<br />
<br />
1. First you'll need to get the right environment and stuff to work with:<br />
:*Get [http://sourceforge.net/projects/mingw/files/Installer/mingw-get-inst MinGW].<br />
:*Install it.<br />
:*Get [http://sourceforge.net/projects/mingw/files/MSYS/Base/msys-core/msys-1.0.11/MSYS-1.0.11.exe/download MSYS] (when installing MSYS answer y, y and input the directory where you installed MinGW when asked).<br />
:*Get [http://mpir.org/mpir-2.5.1.tar.bz2 MPIR] and [https://gforge.inria.fr/frs/download.php/30965/ecm-6.4.3.tar.gz GMP-ECM] (don't unpack them, just place them on your desktop).<br />
<br />
2. Open MSYS (there should be a "MSYS" icon on your desktop) and shut it down again.<br />
<br />
3. Now move the MPIR and GMP-ECM to C:\YourMsysDirectory\1.0\home\YourUser\.<br />
<br />
4. Time to open MSYS again. Inside MSYS you'll need to do as shown on this screenshot:<br />
<br />
[[File:GMP-ECM1.jpg|550px|About to press enter]]<br />
<br />
(and to those of you who for some reason can't see the screenshot: Type <code>tar xjvf mpir-2.5.1.tar.bz2</code> and press enter)<br />
<br />
After pressing enter, MSYS should start unpacking MPIR.<br />
<br />
5. Type <code>cd mpir-2.5.1</code> and press enter (to change to your new MPIR directory)<br />
<br />
6. Type <code>./configure --enable-gmpcompat</code> and press enter.<br />
<br />
[[File:GMP-ECM2.jpg|550px|About to press enter again]]<br />
<br />
Now it will probably start configuring a bunch of stuff and you should see a lot of output.<br />
<br />
7. After MSYS is done configuring, type <code>make install</code><br />
<br />
[[File:GMP-ECM3.jpg|550px|I'm still about to press enter]]<br />
<br />
Now MPIR installs itself. This is going to take a little while.<br />
<br />
8. After it's finished, type <code>cd</code> and press enter to go back to your initial directory.<br />
<br />
9. Follow this screenshot:<br />
<br />
[[File:GMP-ECM4.jpg|550px|Guess what I'm about to do...]]<br />
<br />
(Type <code>tar xzvf ecm-6.4.3.tar.gz</code> and press enter)<br />
<br />
Now it'll start unpacking.<br />
<br />
10. Type <code>cd ecm-6.4.3</code> (to get to the new directory)<br />
<br />
11. Do as shown in the screenshot:<br />
<br />
[[File:GMP-ECM5.jpg|550px|About to press enter]]<br />
<br />
(type <code>./configure --with-gmp=/usr/local</code> and press enter)<br />
<br />
Now it will make sure that you get an optimal performance out of your GMP-ECM.<br />
<br />
12. Type 'make' and press enter. This will create your ecm.exe and will take some time.<br />
<br />
13. When it has finished, close MSYS and you should be able to find ecm.exe in the home-directory.<br />
<br />
Now that you have an optimized ecm.exe you'll need to use it either manually on the Cunningham list or as a part of [[ECMclient]].<br />
<br />
Alternatively, you can use [https://mersenneforum.org/showpost.php?p=491307&postcount=458 a script courtesy of ATH] to compile the latest version of GMP-ECM.<br />
<br />
==Changes between ecm-6.4.2 and ecm-6.4.3==<br />
*Fixed bug reported by user "lorgix" on [http://www.mersenneforum.org/showpost.php?p=286385&postcount=280 mersenneforum]<br />
*Use 64-bit value for random seed under Windows<br />
<br />
==External links==<br />
*[http://gforge.inria.fr/projects/ecm/ GMP-ECM download]<br />
[[Category:Software]]<br />
[[Category:Factoring program]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Primality_testing_program&diff=5790Primality testing program2019-08-29T04:55:11Z<p>GeekPrime: /* External links */ +historical software link</p>
<hr />
<div>A '''primality testing program''' is a [[program]] that performs [[Primality test|primality testing]].<br />
<br />
==Comparison==<br />
{| class="wikitable"<br />
|- <br />
! Program !! Numbers tested !! Hardware !! OS !! Link<br />
|-<br />
| [[Prime95|Prime95|MPrime]]<br />
| [[Mersenne number]]s<br/>a &times; b<sup>n</sup>±c (only factoring and [[probable prime|PRP]]-testing)<br />
| x86 CPU <br />
| Windows, Linux, Mac, FreeBSD<br />
|<br />
|-<br />
| [[LLR]]<br />
| k &times; b<sup>n</sup>±c general numbers<br />
|<br />
| Windows, Linux, Mac<br />
| [http://jpenne.free.fr/index2.html]<br />
|-<br />
| [[llrCUDA]]<br />
| k &times; b<sup>n</sup>±c<br />
| CUDA GPU<br />
| Linux<br />
| [http://jpenne.free.fr/index2.html]<br />
|-<br />
| [[CUDALucas]]<br />
| Mersenne numbers<br />
| [[CUDA]] [[GPU]]<br />
| Windows, Linux<br />
|<br />
|-<br />
| [[clLucas]]<br />
| Mersenne numbers<br />
| [[OpenCL]] GPU<br />
|<br />
|<br />
|-<br />
| [[gpuOwL]]<br />
| Mersenne numbers<br />
| OpenCL GPU<br />
|<br />
|<br />
|-<br />
| [[Mlucas]]<br />
| Mersenne numbers<br />
| x86 CPU<br/>ARM CPU<br />
|<br />
|<br />
|-<br />
| [[Glucas]]<br />
| Mersenne numbers<br />
| CPU<br />
|<br />
|<br />
|-<br />
| [[PFGW]]<br />
| general numbers<br />
| x86 CPU<br />
| Windows, Linux, Mac<br />
| [http://sourceforge.net/projects/openpfgw/]<br />
|-<br />
| [[Phrot]]<br />
| k &times; b<sup>n</sup>±1<br />
|<br />
|<br />
| [http://home.roadrunner.com/~mrodenkirch/home/Phrot.html]<br />
|-<br />
| [[Genefer]]<br />
| [[generalized Fermat number]]s<br />
| CPU<br />
| Windows<br />
| [http://home.roadrunner.com/~mrodenkirch/home/Genefer.html], [http://www.underbakke.com/genefer/]<br />
|-<br />
| [[GeneferCUDA]]<br />
| [[generalized Fermat number]]s<br />
| CUDA GPU<br />
|<br />
| [http://mersenneforum.org/showthread.php?t=14297]<br />
|-<br />
| [[Primo]]<br />
| general numbers<br />
| 64-bit CPU<br />
| Linux<br />
| [http://www.ellipsa.eu/public/primo/primo.html]<br />
|-<br />
| [[ECPP-DJ]]<br />
| general numbers<br />
| CPU<br />
| <br />
| [https://github.com/danaj/Math-Prime-Util-GMP]<br />
|-<br />
| [[Proth.exe|Proth]]<br />
| k &times; b<sup>n</sup>±1<br />
|<br />
| Windows<br />
| [http://primes.utm.edu/programs/gallot/index.html]<br />
|-<br />
| [[MPZ APR-CL]]<br />
| general numbers<br />
| CPU<br />
|<br />
| [https://sourceforge.net/projects/mpzaprcl/]<br />
|-<br />
| [[Pock]]<br />
| primality testing by [[Pocklington's theorem]]<br />
|<br />
|<br />
| [http://homepage2.nifty.com/m_kamada/math/pock.htm]<br />
|-<br />
| [[Maclucas.cuda]]<br />
| Mersenne numbers<br />
| CUDA GPU<br />
|<br />
| [http://www.mersenneforum.org/showthread.php?t=12576]<br />
|}<br />
<br />
==External links==<br />
*[http://mersenneforum.org/showthread.php?t=3255 Mersenneforum section on factoring programs links] contains several links to primality testing programs.<br />
*[https://www.mersenne.org/download/freeware.php Mersenne Prime Freeware] by [[Luke Welsh]] and Yuri Sorkin. Last updated on April 3, 2008.<br />
<br />
[[Category:Primality testing program| ]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=User:GeekPrime&diff=5770User:GeekPrime2019-08-21T14:57:17Z<p>GeekPrime: </p>
<hr />
<div>{{#babel:uk-N|en-3|zh-1}}<br />
GIMPS team: [[Top GIMPS teams|UKRAINE]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=James_Heinrich&diff=5765James Heinrich2019-08-21T14:48:53Z<p>GeekPrime: according to https://www.mersenne.org/legal/ the system admin is Blosser; forgive me if I am wrong</p>
<hr />
<div>{{Infobox Person<br />
| Name=James Heinrich<br />
| More=y<br />
| MersForum=1085 James Heinrich<br />
| Website=http://www.mersenne.ca/ mersenne.ca<br />
}}<br />
<br />
'''James Heinrich''' is a website administrator of the [[PrimeNet server]] (along with [[Aaron Blosser]]).[https://www.mersenne.org/legal/]<br />
<br />
He is also the maintainer of [[mersenne.ca]], which mirrors the data on the PrimeNet server, and coordinates the search of factors of Mersenne numbers with exponents between 1G and 10G (which includes [[Operation Billion Digits]]).</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=George_Woltman&diff=5763George Woltman2019-08-21T14:40:49Z<p>GeekPrime: </p>
<hr />
<div>{{Infobox Person<br />
| Name=George Woltman<br />
| Born=1957-11-10<br />
| Nationality=American<br />
| Wikipedia=George_Woltman<br />
| More=y<br />
| MersForum=4 Prime95<br />
| Top5000=44 George F. Woltman<br />
| Website=https://www.mersenne.org/ GIMPS Homepage<br />
}}<br />
'''George Woltman''' is the founder of the [[Great Internet Mersenne Prime Search]] (GIMPS), a [[:Category:distributed computing project|distributed computing project]] researching [[Mersenne prime]] numbers using his software [[Prime95]] and [[Prime95|MPrime]]. He graduated from the [[Massachusetts Institute of Technology]] (MIT) in 1978 with degrees in Computer Science, and is presently living in Orlando, Florida. His mathematical libraries created for the GIMPS project are the fastest known for [[multiplication]] of large [[integer]]s, and are also used by other distributed computing projects.<br />
<br />
He has been on the board of [[Mersenne Research, Inc.]] since 2008, and currently serves as President and Treasurer of the organization.<br />
<br />
==See also==<br />
*[[Great Internet Mersenne Prime Search]]<br />
*[[Prime95]]<br />
*[[Prime95|MPrime]]<br />
<br />
==External links==<br />
*[http://primes.utm.edu/bios/page.php?id=44 The Prime Pages Titan Biography]<br />
*[https://en.wikipedia.org/wiki/George_Woltman Wikipedia article]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Great_Internet_Mersenne_Prime_Search&diff=5762Great Internet Mersenne Prime Search2019-08-21T14:37:31Z<p>GeekPrime: </p>
<hr />
<div>{{Shortcut|GIMPS|Great Internet Mersenne Prime Search: A [[distributed computing project]] for the search of [[Mersenne prime]]s.}}<br />
The '''Great Internet Mersenne Prime Search''', also known as '''GIMPS''', is a prime example of [[distributed computing]] project at work and no pun intended. It is a [[:Category:Distributed computing project|collaborative project]] of volunteers, who use [[Prime95]], software that can be downloaded from the Internet, in order to search for [[Mersenne prime]] numbers.<br />
<br />
Mersenne primes are named after [[Marin Mersenne]], a French monk and mathematician, who was born in 1588. Mersenne investigated a particular type of prime numbers: 2<sup>p</sup> - 1, in which ''p'' is an ordinary [[prime]].<br />
<br />
Mersenne primes are much rarer than ordinary primes, of which there are an infinite number. The GIMPS effort, exhaustively searching for possible candidates since 1996, has been responsible for discovering the largest Mersenne Primes to date. See the [[list of known Mersenne primes]] for more details.<br />
<br />
This project has been rather successful: it has found 17 [[Mersenne prime]]s, each of which was the largest known prime at the time of discovery. The largest currently known prime is {{Greatest Mersenne Prime|text}}. Refer to the article on Mersenne primes for the complete list of GIMPS successes.<br />
<br />
The project was founded by [[George Woltman]], who also wrote the [[Primality testing program|prime testing software]] [[Prime95]]. The GIMPS project was formed in January 1996. [[Scott Kurowski]] wrote the [[PrimeNet]] server software that supports the research to demonstrate Entropia distributed computing software, a company he founded in 1997. In 2008, a legal entity was registered to administer GIMPS – [[Mersenne Research, Inc.]]<br />
<br />
The [[Electronic Frontier Foundation]] (EFF) offered $100,000 to the first person(s) who discovered a [[ten million digits]] prime. GIMPS claimed this award. The owner of the discovering computer received $50,000 from the GIMPS foundation.<br />
<br />
Although the GIMPS software has its source code available, technically it is not [[open source]], since it has a restriction which most open source/free software groups find unacceptable &ndash; users must abide by the prize distribution terms. This restriction will become meaningless when the EFF [[EFF prizes|prizes]] are claimed.<br />
<br />
For open source alternatives, [[Mlucas]] and [[Glucas]] are both licensed under the GPL.<br />
<br />
Most GIMPS members [[Why_participate_in_GIMPS?|join the search]] for the thrill of possibly discovering a record-setting, rare, and historic, new Mersenne prime. All you have to do to be part of it, is to contribute spare or idle CPU cycles. Pretty cool.<br />
<br />
If you want to know more, there is a [[:Category:GIMPS FAQ|GIMPS FAQ]] available in this wiki.<br />
<br />
==External links==<br />
* [http://www.mersenne.org/ GIMPS Home Page]<br />
* [http://www.mersenneforum.org/ GIMPS Forum]<br />
* [http://mersenne.org/primenet/ PrimeNet server]<br />
{{Navbox GIMPS}}<br />
{{Navbox Projects}}<br />
[[Category:Great Internet Mersenne Prime Search| ]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=User:GeekPrime&diff=5761User:GeekPrime2019-08-21T14:33:26Z<p>GeekPrime: </p>
<hr />
<div>GIMPS team: [[Top GIMPS teams|Ukraine]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Ernst_Mayer&diff=5760Ernst Mayer2019-08-21T14:31:39Z<p>GeekPrime: </p>
<hr />
<div>'''Ernst W. Mayer''' is an American programmer and scientist. He is the author of the [[Mlucas]] program, which has been frequently used to independently verify newly discovered [[Mersenne prime]]s.<br />
<br />
He received his Ph.D. (1993) in Aerospace Engineering from the University of Michigan, Ann Arbor.<br />
<br />
He is also the author of "emayer" [[Fast Fourier transform|FFT]] package, written in Fortran 90, which was used to benchmark [[FFTW]] library.<br />
<br />
He has been on the Board of Directors of [[Mersenne Research, Inc.]] since January 2019.<br />
<br />
==Patents==<br />
*7,725,863 [http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=7725863.PN.&OS=PN/7725863&RS=PN/7725863 Reverse Routing Methods for Integrated Circuits Having an Hierarchical Interconnect Architecture], Granted 25 May 2010.<br />
*7,786,757 [http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=7786757.PN.&OS=PN/7786757&RS=PN/7786757 Integrated Circuits with Hybrid Planar Hierarchical Architecture and Methods for Interconnecting Their Resources], Granted 31 August 2010.<br />
<br />
==External links==<br />
*[http://www.mersenneforum.org/mayer/home.html Ernst W. Mayer &ndash; Homepage]<br />
*[http://www.mersenneforum.org/mayer/resume.html Ernst W. Mayer &ndash; Résumé]<br />
[[Category:Person|Mayer, Ernst]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Mersenne_Research,_Inc.&diff=5757Mersenne Research, Inc.2019-08-21T14:29:44Z<p>GeekPrime: </p>
<hr />
<div>'''Mersenne Research, Inc.''' is a non-profit corporation charitably organized to promote and conduct mathematical and computer science research and support related education within the meaning and limits of U.S. Internal Revenue Code 501(c)(3), and the State of California Revenue and Taxation Code.<br />
<br />
Mersenne Research owns and operates web content, data and software of the [[Great Internet Mersenne Prime Search]] available at [[Mersenne.org]].<br />
<br />
== Board of Directors ==<br />
'''2008–2019''': [[Scott Kurowski]], [[George Woltman]], [[Luke Welsh]].<br />
<br />
'''2019''': [[George Woltman]], [[Luke Welsh]], [[Ernst Mayer]].<br />
<br />
== Links ==<br />
* [https://www.mersenne.org/legal/ GIMPS by Mersenne Research, Inc.]<br />
* [https://www.mersenneforum.org/showthread.php?p=513887 GIMPS Board January 2019 meeting]<br />
<br />
[[Category:Organizations]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Luke_Welsh&diff=5756Luke Welsh2019-08-21T14:25:52Z<p>GeekPrime: Created page with "'''Luke Welsh''' is an American programmer and businessman. In 1988, he co-discovered the 29th Mersenne prime. He has been on the Board of Directors of Mersenne R..."</p>
<hr />
<div>'''Luke Welsh''' is an American programmer and businessman.<br />
<br />
In 1988, he co-discovered the [[M29|29th Mersenne prime]].<br />
<br />
He has been on the Board of Directors of [[Mersenne Research, Inc.]] since 2008.<br />
<br />
== Link ==<br />
*[https://www.linkedin.com/in/luke-welsh-a1545b25/ Luke Welsh] on LinkedIn.<br />
<br />
[[Category:Person]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Mersenne_Research,_Inc.&diff=5755Mersenne Research, Inc.2019-08-21T14:13:24Z<p>GeekPrime: Created page with "'''Mersenne Research, Inc.''' is a non-profit corporation charitably organized to promote and conduct mathematical and computer science research and support related education..."</p>
<hr />
<div>'''Mersenne Research, Inc.''' is a non-profit corporation charitably organized to promote and conduct mathematical and computer science research and support related education within the meaning and limits of U.S. Internal Revenue Code 501(c)(3), and the State of California Revenue and Taxation Code.<br />
<br />
Mersenne Research owns and operates web content, data and software of the [[Great Internet Mersenne Prime Search]] available at [[Mersenne.org]].<br />
<br />
== Board of Directors ==<br />
'''2010''': [[Scott Kurowski]], [[George Woltman]], [[Luke Welsh]].<br />
<br />
'''2019''': [[George Woltman]], [[Luke Welsh]], [[Ernst Mayer]].<br />
<br />
== Links ==<br />
* [https://www.mersenne.org/legal/ GIMPS by Mersenne Research, Inc.]<br />
<br />
[[Category:Organizations]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=PrimeNet_server&diff=5754PrimeNet server2019-08-21T14:05:25Z<p>GeekPrime: added new administrators, moved old info into sections</p>
<hr />
<div>The '''PrimeNet server''' is the machine that is the hub of operations for [[GIMPS]].<br />
<br />
Previously the server was maintained by [[Scott Kurowski]]. Later the system administration was taken over by [[Aaron Blosser]], and site maintenance (''Mersenne.org'') by Aaron Blosser and [[James Heinrich]].<br />
<br />
== PrimeNet vs PrimeNet server ==<br />
While sometimes used synonymously, [[PrimeNet]] and the PrimeNet server are two different things. The PrimeNet server is a physical [[computer]] with a specific location. PrimeNet is the [[software]] that GIMPS uses to co-ordinate work and the associated data.<br />
<br />
== 2008 PrimeNet server crash and V5 upgrade ==<br />
About the time that [[M45]] and [[M47]] were found, the existing PrimeNet server crashed. The new server was brought online along with a new version of the PrimeNet software (v.5).[https://www.mersenneforum.org/showthread.php?t=11022][https://www.mersenneforum.org/showthread.php?t=10832] (The software had been in developement, as had been a new version of [[Prime95]] that was being readied to be rolled out at the same time.) With the arrival of the new server and both software packages, the range of GIMPS [[exponent]]s being handled by PrimeNet increased from [[79.3 million]] to 999,999,999.<br />
<br />
While the crash may have seemed to have come at the worst possible time (the discovery of 2 new [[prime]]s in quick succession), the new software forced into service has had important benefits. Since one of the 2 new primes was 10 million decimal digits long, it qualified for one of the [[EFF prizes]]. This lead to a raised interest in the EFF prize for the first 100 million digit prime. With the expanded range PrimeNet could now host the work being done in the [[100 Million Digit Prefactor Project]]. Also, many that were doing [[Lone Mersenne Hunters]] work, could now report directly to PrimeNet server and not manually to [[George Woltman]]. Another benefit is the many new [[GIMPS PrimeNet reports|reports]] that can be generated easily. These can be used for a variety of purposes including LMH. Also, the [[GIMPS statistics]] have been updated to a newer unit [[Computing power#GHz-days|GHz-days]] and no longer [[Computing power#P90 years|P90 years]]. Further, the addition of better [[account]] controls and more [[worktype]]s have been a helpful. Better [[manual assignment]] handling has been added too.<br />
<br />
== Link ==<br />
* [https://www.mersenne.org/ PrimeNet]<br />
<br />
{{Navbox GIMPS}}<br />
[[Category:Great Internet Mersenne Prime Search]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=M47&diff=5748M472019-08-21T13:17:44Z<p>GeekPrime: added link to EFF prize claim for Mersenne Research, Inc.</p>
<hr />
<div>{{InfoboxMersennePrime<br />
| title=M47<br />
| rank=47<br />
| nvalue=43112609<br />
| top5000id=85527<br />
| digits=12978189<br />
| pdigits=25957378<br />
| number=316470269330...166697152511<br />
| discovery=2008-08-23<br />
| discoverer=[[Edson Smith]]<br />
| foundwith=[[Lucas-Lehmer test]];[[Prime95]] on Dell Optiplex 745<br />
| credits=[[George Woltman]];[[Scott Kurowski]] et al.;([[GIMPS]] & [[PrimeNet]])<br />
}}<br />
'''M47''' normally refers to the 47th [[Mersenne prime]] 2<sup>{{Num|43112609}}</sup>-1, in order of size from the smallest to greatest. This is the primary usage and what is refered to in the rest of this article. For clarification about other possible usages refer to the [[Nomenclature and notation]] article. The number now refered to as M47 was actually the 45th Mersenne prime found. [[M45]], [[M46]], and M47 were discovered in the order of M47, M45 (2 weeks later), then M46 (8 months later).<br />
<br />
On 2018-04-08 all tests below 2<sup>{{Num|43112609}}</sup>-1 were verified by [[GIMPS]], officially making it the 47th Mersenne prime.<br />
<br />
==Discovery==<br />
On 2008-08-23 a Dell Optiplex 745 [[computer]], running [[Prime95]], completed the [[Lucas-Lehmer test]] for the number 2<sup>{{Num|43112609}}</sup>-1 and found out that it was a [[prime]] number. The computer was stationed at a lab in the Mathematics Department at [[University of California, Los Angeles]].<br />
<br />
Upon discovery, an audio alert was activated and an automatic notification was sent to [[PrimeNet]]. PrimeNet sent an automatic e-mail to [[George Woltman]]. He then contacted [[Edson Smith]], who lead the team at UCLA.<br />
<br />
This was the first prime found larger than [[ten million digits]], it has {{Num|12978189}} [[decimal]] digits.<br />
<br />
==Verification==<br />
To confirm that there were no errors in the [[hardware]] (such as the [[Pentium Bug]] or a random bit error or [[software]], the number had to be verified by running the Lucas-Lehmer test on at least one different machine (not just a separate physical computer, but one based upon a different [[CPU]] [[architecture]]) and using a different [[program]].<br />
<br />
As a very quick check against errors, George Woltman obtained a "[[GIMPS client files|save file]]" from Edson Smith and re-ran the last few thousand [[iterations]] on one of his machines. No problems were detected. He also started testing the exponent on one of his machines. (Even though it used a similar processor and the same software, this step was useful for finding potential errors before the test was complete.) George notified a select group of volunteers that have access to much faster computers. They started verification runs using these different types of computers and different software. They are:<br />
<br />
*Tony Reix (France) of [[Bull S.A.]] running [[Glucas]] (written by [[Guillermo Ballester]]) on 16 1.6GHz Itanium2 CPUs of a Bull NovaScale 6160 HPC server in Grenoble<br />
*Jeff Gilchrist (Canada) ran Glucas on up to 16 1.6 GHz Itanium2 CPUs of a server at [[SHARCNET]] in Ottawa.<br />
*Tom Duell (USA) and Rob Giltrap (New Zealand), both of Sun Microsystems, using [[Mlucas]] doing 2 separate runs:<br />
**One on 8 dual-core SPARC64 VI 2.15Ghz CPUs of a [[Sun]] [[SPARC]] Enterprise M5000 Server<br />
**One on 4 quad-core SPARC64 VII 2.52GHz CPUs of a Sun SPARC Enterprise M8000 Server<br />
:The machines were in Menlo Park, California, USA. These were the first verifications completed and took 13 days.<br />
<br />
Throughout the verification runs, the [[residue]] values were exchanged amongst the various individuals. If they did not match, an error would have been indicated. This is were George's run with Prime95 (although slower) was useful. If his check had shown up different than the others, it would have indicated a problem with either his software or hardware.<br />
<br />
==Prize==<br />
This was the first prime number, of any sort, found larger than {{Num|10000000}} digits. The [[Electronic Frontier Foundation]] had an established [[EFF prizes|${{Num|100000}} prize]] for the first prime greater than {{Num|10000000}} digits. GIMPS claimed the prize and divide it with ${{Num|50000}} going to UCLA, ${{Num|25000}} going to a charity, and the remainder being used by GIMPS to provide awards to other finders of Mersenne primes and to cover expenses.<br />
<br />
==External Links==<br />
*[http://newsroom.ucla.edu/stories/081008_mersenne-prime Article at UCLA]<br />
*[http://www.math.ucla.edu/~edson/prime/ Edson Smith and primes]<br />
*[http://www.mersenne.org/primes/m45and46.htm GIMPS Discovers 45th and 46th Mersenne Primes, 2<sup>43,112,609</sup>-1 is now the Largest Known Prime]. Press-release.<br />
*[https://www.eff.org/awards/coop/primeclaim-43112609 Mersenne Research, Inc.'s 2009 claim for 2<sup>43112609</sup>-1]. [[Electronic Frontier Foundation|EFF]].<br />
<br />
[[Category:Mersenne prime]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Probable_prime&diff=5746Probable prime2019-08-21T12:51:50Z<p>GeekPrime: </p>
<hr />
<div>{{Shortcut|PRP|Probable prime: an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers.}}<br />
In [[number theory]], a '''probable prime''' (PRP) is an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers. Different types of probable primes have different specific conditions. While there may be probable primes that are [[Composite number|composite]] (called [[pseudoprime]]s), the condition is generally chosen in order to make such exceptions rare.<br />
<br />
'''Fermat's test for compositeness''' (sometimes called '''Fermat primality test''') is based on [[Wikipedia:Fermat%27s_little_theorem|Fermat's little theorem]]. It works as follows:<br />
:Given an integer ''n'', choose some integer ''a'' [[coprime]] to ''n'' and calculate an <math>a^n \equiv 1</math> [[Modular arithmetic|modulo]] ''n''. If the result is different from 1, ''n'' is composite. If it is 1, ''n'' may or may not be prime; ''n'' is then called a (weak) probable prime to base ''a''.<br />
<br />
Therefore Fermat's test can definitively tell only if a number is composite. Otherwise, if the test is not indicating compositeness, applying another primality test (like [[Lucas-Lehmer test]]) will be needed to find out if the number is really composite or not.<br />
<br />
==External links==<br />
*[[Wikipedia:Probable_prime|Probable prime]]<br />
*[http://www.primenumbers.net/prptop/prptop.php PRP Records] maintained by H.& R. Lifchitz<br />
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{{Navbox NumberClasses}}<br />
<br />
[[Category:Math]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Aaron_Blosser&diff=5744Aaron Blosser2019-08-21T12:04:55Z<p>GeekPrime: </p>
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<div>{{Stub}}<br />
{{Infobox Person<br />
| Name=Aaron Blosser<br />
}}<br />
'''Aaron Blosser''' is a system administrator of [[PrimeNet]].<br />
<br />
He is listed as co-discoverer of [[M49]], [[M50]] and [[M51]] Mersenne primes.</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=CUDALucas&diff=5741CUDALucas2019-08-21T11:11:04Z<p>GeekPrime: </p>
<hr />
<div>{{InfoboxProgram|title=CUDALucas|workload=[[Lucas-Lehmer test]]|release=2009|latest=2.06beta<br>2017-05-05}}<br />
'''CUDALucas''' is a [[CUDA]]-based program written by [[Shoichiro Yamada]] for testing [[Mersenne number]]s for primality with [[Lucas-Lehmer test]].<br />
<br />
CUDALucas is a sophisticated implementation of the [[Irrational base discrete weighted transform|IBDWT]] method for [[GPU]]. It has been developed by Yamada as a direct port of the highly optimized sequential [[MacLucasFFTW]], itself a port to FFTW of a program tracing its roots back to original code by [[Richard Crandall]] et al.[http://www.ece.neu.edu/groups/nucar/GPGPU4/files/thall.pdf]<br />
<br />
The program was used to verify primes [[M48]], [[M49]], [[M50]] and [[M51]] at the times of their discovery.<br />
<br />
==Tuning==<br />
To improve performance of CUDALucas, you need to run two benchmarks for your GPU. For example, like this:<br />
<br />
CUDALucas -cufftbench 1 22680 5<br />
CUDALucas -threadbench 1 22680 5 10<br />
<br />
These commands will generate files <code>DEVICENAME fft.txt</code> and <code>DEVICENAME threads.txt</code>, enabling CUDALucas to select the parameters for an exponent being tested more efficiently.<br />
<br />
==Integrity checks==<br />
To ensure that your program and GPU are working properly, you need to run self tests. For example, like this:<br />
<br />
CUDALucas -r 1<br />
CUDALucas -memtest 40 1<br />
CUDALucas 1398269<br />
<br />
Option <code>-r 1</code> will run a thorough (long) self test. Option <code>-memtest 40 1</code> will run a short version of memory test for 1 GB (a few hours test is advised, however). The command <code>CUDALucas 1398269</code> will test [[M35]] for primality.<br />
<br />
==External links==<br />
*[http://mersenneforum.org/showthread.php?t=12576 CUDALucas thread] at [[MersenneForum]]<br />
*[http://sourceforge.net/projects/cudalucas/ CUDALucas] at SourceForge<br />
*[https://sourceforge.net/projects/cudalucas/files/ CUDALucas README]<br />
*[https://www.mersenne.ca/cudalucas.php GPU benchmarks with CUDALucas/clLucas]<br />
[[Category:Software]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=Mlucas&diff=5740Mlucas2019-08-21T11:09:06Z<p>GeekPrime: </p>
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<div>{{InfoboxProgram<br />
|title=Mlucas<br />
|workload=[[Lucas-Lehmer test|LL]]<br />
|release=< 1999<br />
|latest=18.0<br><small>03-06-2019</small><br />
}}<br />
<br />
'''Mlucas''' is a program for performing [[Lucas-Lehmer test]]s of prime-exponent [[Mersenne number]]s. It is written by [[Ernst Mayer]] using C programming language and [[ARM]] assembly. It also includes an optional Python script for assignment management for the [[GIMPS]] project's [[PrimeNet]] server.<br />
<br />
Mlucas is an open-source program and, unlike [[George Woltman]]'s [[Prime95]], does not impose prize-sharing rules, should a user be lucky as to find a new prime eligible for the monetary prize offered by the [[Electronic Frontier Foundation]].<br />
<br />
Mlucas includes optimizations for processors supporting [[Advanced Vector Extensions|AVX-512, AVX2, AVX]], SSE2 or ARMv8 SIMD instruction sets.<br />
<br />
As of June 2017, Mlucas v17.0 run only about 10% slower than Prime95 on powerful hardware.<br />
<br />
The program was used to verify primes [[M38]], [[M45]], [[M46]], [[M47]], [[M48]], [[M49]], [[M50]] and [[M51]] at the times of their discovery.<br />
<br />
==External links==<br />
*[http://www.mersenneforum.org/mayer/README.html Mlucas homepage]<br />
*[http://www.mersenneforum.org/forumdisplay.php?f=118 Mlucas subforum] at [[MersenneForum]]<br />
[[Category:Software]]</div>GeekPrimehttps://www.rieselprime.de/z/index.php?title=M51&diff=5739M512019-08-21T11:07:49Z<p>GeekPrime: </p>
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<div>{{InfoboxMersennePrime<br />
| title=M51<br />
| rank=51<br />
| nvalue=82589933<br />
| top5000id=125874<br />
| digits=24862048<br />
| pdigits=49724095<br />
| number=148894445742...325217902591<br />
| discovery=2018-12-07<br />
| discoverer=[[Patrick Laroche]]<br />
| foundwith=[[Lucas-Lehmer test]];[[Prime95]] on Intel i5-4590T @ 2.0GHz<br />
| credits=[[George Woltman]];[[Aaron Blosser]] et. al.;([[GIMPS]] & [[PrimeNet]])<br />
}}<br />
'''M51''' normally refers to the 51th [[Mersenne prime]], in order of size from the smallest to greatest. This is the primary usage and what is referred to in the rest of this article.<br />
<br />
==Discovery==<br />
The official discovery date for prime {{Greatest Mersenne Prime|only}} was 2018-12-21 and has {{Num|24862048}} [[digit]]s.<br />
<br />
A computer volunteered by [[Patrick Laroche]] made the find on 2018-12-07. The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU.<br />
<br />
The official credit for the discovery goes to "P. Laroche, [[George Woltman|G. Woltman]], [[Aaron Blosser|A. Blosser]], et al.".<br />
<br />
==Verification==<br />
To confirm that there were no errors in the [[hardware]] or [[software]], the number had to be independently verified by running tests on various machines with different architecture and software.<br />
<br />
The volunteers that ran these tests were:<br />
*Andreas Höglund verified the prime using [[CUDALucas]] running on a NVidia V100 GPU in 21 hours.<br />
*Andreas Höglund also verified the prime using [[Mlucas]] running on 16 cores of an Amazon AWS instance in 72 hours.<br />
*Aaron Blosser also verified it using [[Prime95]] on an Intel 7700K processor in 6 days, 8 hours.<br />
<br />
==External links==<br />
*[https://www.mersenne.org/primes/?press=M82589933 Official press release by GIMPS]<br />
*[https://www.mersenneforum.org/showthread.php?t=23877 Discovery thread] at [[MersenneForum]]<br />
<br />
[[Category:Mersenne prime]]</div>GeekPrime