Seit März 2019 rechnet ein Intel-NUC mit Intel(R) Core(TM) i7-8559U CPU an den Primzahlen, allerdings gedrosselt, da sonst der Stromverbrauch zu hoch ist. Dadurch erreiche ich nochmal einen etwa 50% geringeren Stromverbrauch bei gleicher Rechenleistung gegenüber dem vorhergehenden PC. Folgende ältere Rechner haben bisher beigetragen:

- Von Mai 2011 bis Februar 2019 rechnete ein Desktop-PC mit Intel(R) Core(TM) i3-2100T (SandyBridge) an den Primzahlen; Dieser Rechner verbrauchte ca. 600kWh Strom im Jahr weniger als der Vorhergehende!
- Von Februar 2007 bis April 2011 rechnete ein Desktop-PC mit AMD Athlon(TM) 64 X2 Dual Core Processor 3800+ an den Primzahlen
- Von Juni 1999 bis Januar 2007 rechnete ein Desktop-PC mit Intel(R) Pentium(TM) II 450 MHz mit 2 Prozessoren an den Primzahlen

Insgesamt rechne ich beim GIMPS-Projekt seit Juni 1999 mit. Schliesslich
bot die EFF (Electronic Frontier Foundation) ein Preisgeld von 100 000 US$ für denjenigen,
der die erste Primzahl mit mehr als 10 Mio. Stellen berechnet.

Der Preis wurde an das Mathematics Department der University of California, Los Angeles (UCLA) vergeben.
Dort wurde in 2008 mit Hilfe der GIMPS-Software eine Primzahl mit mehr als 12 Millionen Stellen gefunden (siehe auch
http://www.eff.org/press/archives/2009/10/14-0). Es sind neue Preise ausgeschrieben worden:
*$150,000 to the first individual or group who discovers a prime with at least 100 million digits, and $250,000 for a prime with at least a billion digits*.

Aktuelle Computer haben die Rechenleistung, um z.B. die P-1 Berechnung an 11-Mio-Exponenten in zwei bis drei Wochen durchzuführen, der CERT- Check dauert nur wenige Stunden.

Für viele Jahre wurden im GIMPS-Projekt Lucas-Lehmer-Tests ausgefürt, wobei zunächst geprüft wurde, ob es Faktoren
gibt, die kleiner als 2^68 sind. Manchmal wurden welche gefunden, diese sind in der nachfolgenden Liste mit dabei. Ebenfalls angegeben sind Exponenten, die doppelt überprüft worden sind (double-check). Diese wurden früher auf einem anderen Rechner ein zweites Mal per Lucas-Lehmer-Test gerechnet, um sicher zu sein, dass kein Berechnungsfehler vorliegt.

Neuerdings hat sich aufgrund eines mathematischen Durchbruchs die Methodik geändert. Im ersten Schritt (P-1) wird ein Test ausgeführt, bei dem ein Prüf-File mitgeschrieben wird (PRP proof). Im zweiten Schritt wird anhand von Zertifikaten überprüft, ob die Berechnung in P-1 einwandfrei war mit einem Bruchteil der Rechenzeit (completed CERT check).

- Mersenne Primes Homepage
- Alle bekannten Mersenne-Primzahlen
- Krzysztof Pietrzak: Simple Verifiable Delay Functions (Durchbruch in der Mathematik mit der Konsequenz, dass die double-checks entfallen können, stattdessen werden die CERT checks in 0,5% der Rechenzeit eines LL-Tests durchgeführt

Die folgenden 560 Exponenten haben meine Rechner bisher getestet (das M steht für Mersenne-Exponent):

M2216281 completed CERT check M2264183 completed CERT check M2632793 completed CERT check M4317409 completed CERT check M5538167 completed CERT check M5655619 completed CERT check M6535673 is not prime M8074309 completed CERT check M8269691 is not prime M8444609 completed CERT check M8551733 is not prime M8711669 is not prime M8713631 is not prime M8801951 is not prime M8988583 is not prime M9117601 is not prime M9144787 is not prime M9274879 completed CERT check M9498023 is not prime M9506459 is not prime M9591983 is not prime M9730711 is not prime M9806681 has two factors: 1476527692851550543, 862371638037584273 M9987433 is not prime M10035989 is not prime M10069679 is not prime M10089929 is not prime M10229603 is not prime M10236097 is not prime M10241743 is not prime M10262909 is not prime M10263233 is not prime M10290263 is not prime M10325687 is not prime M10378813 is not prime M10437547 is not prime M10513333 is not prime M10593647 is not prime M10654123 is not prime M10669837 is not prime M10697567 is not prime M10713877 is not prime M10784167 is not prime M10799381 completed CERT check M10839953 has a factor: 1251974034391382088361 M10849079 is not prime M10901167 is not prime M10910279 is not prime M11137739 is not prime M11142881 has a factor: 1194314131589894174257 M11170703 is not prime M11420567 is not prime M11596633 completed CERT check M11603773 completed CERT check M11667683 is not prime M11685991 completed CERT check M11740441 completed CERT check M11790991 is not prime M11794813 completed CERT check M11884267 is not prime M11918521 completed CERT check M11931407 completed CERT check M11972159 is not prime M12004117 completed CERT check M12058357 is not prime M12122879 completed CERT check M12165787 is not prime M12173237 is not prime M12230221 is not prime M12246677 completed CERT check M12255889 completed CERT check M12268693 completed CERT check M12280687 is not prime M12289009 completed CERT check M12374737 is not prime M12434483 is not prime M12524177 is not prime M12593681 is not prime M12635251 is not prime M12802399 completed CERT check M12820849 completed CERT check M12847349 is not prime M12909077 completed CERT check M12930067 is not prime M12939811 completed CERT check M13000979 completed CERT check M13069439 completed CERT check M13099717 is not prime M13147327 is not prime M13170679 completed CERT check M13194959 completed CERT check M13206257 is not prime M13206343 completed CERT check M13239469 is not prime M13247873 completed CERT check M13252373 completed CERT check M13276409 completed CERT check M13364899 completed CERT check M13370761 completed CERT check M13382459 is not prime M13416593 completed CERT check M13455527 completed CERT check M13541039 completed CERT check M13541417 is not prime M13579463 completed CERT check M13614539 completed CERT check M13747879 is not prime M13755769 completed CERT check M13756807 completed CERT check M13802951 completed CERT check M13823959 completed CERT check M13825351 completed CERT check M13868051 completed CERT check M13871579 completed CERT check M13875677 is not prime M13927211 completed CERT check M13942237 completed CERT check M13953997 completed CERT check M13958333 is not prime M13987621 completed CERT check M13996379 completed CERT check M14001019 completed CERT check M14016829 completed CERT check M14047387 completed CERT check M14052091 completed CERT check M14058361 completed CERT check M14069039 is not prime M14072659 is not prime M14167717 is not prime M14190271 is not prime M14457607 is not prime M14473729 is not prime M14885639 is not prime M15213287 is not prime M15395033 is not prime M15546847 is not prime M15801319 is not prime M15878059 is not prime M15965311 is not prime M16150609 is not prime M16588633 is not prime M16624661 is not prime M16883903 is not prime M16899041 is not prime M16920107 is not prime M17000479 completed CERT check M17036233 is not prime M17138917 is not prime M17282563 is not prime M17510371 is not prime M17564681 is not prime M17711143 has a factor: 11811068152556338975780399 M18000869 completed CERT check M22504201 is not prime M22784383 is not prime M23309647 is not prime M23564419 is not prime M23747183 is not prime M24554141 is not prime M24613541 is not prime double-check M24647813 is not prime double-check M24809621 is not prime double-check M24865703 is not prime M24872191 is not prime double-check M24878551 is not prime M25150663 is not prime double-check M25198933 is not prime double-check M25304233 is not prime M25340267 is not prime double-check M25455217 is not prime double-check M25654963 is not prime double-check M25833007 is not prime double-check M26148643 is not prime M26283079 is not prime double-check M26374987 is not prime double-check M26436721 is not prime double-check M26848769 is not prime double-check M26869897 is not prime double-check M27153211 is not prime double-check M27439793 is not prime double-check M27540859 is not prime double-check M28666283 is not prime M30782929 is not prime M30846461 is not prime M32065081 is not prime M32886943 is not prime M33120473 is not prime M34233847 is not prime M36019699 is not prime M36020947 is not prime M36416411 is not prime M36836927 is not prime M37013023 is not prime M37408457 is not prime M37416857 is not prime M37441879 is not prime M37723247 is not prime M37938217 is not prime double-check M38004871 is not prime M38117773 is not prime M38138383 is not prime M39065941 has a factor: 5319303994519034545231 M39176227 is not prime M39444073 is not prime M39584047 is not prime M39607889 is not prime M39732079 is not prime M40030867 is not prime M40062091 is not prime M40442471 is not prime M40677677 is not prime M41494339 is not prime M41642729 is not prime double-check M41660159 is not prime double-check M41661811 has a factor: 648777276331488364129 M41796449 is not prime double-check M41986793 is not prime double-check M42508859 is not prime M42735089 is not prime M43171159 is not prime M43196389 is not prime double-check M44282531 is not prime M44335619 is not prime M44403497 is not prime M44563327 is not prime M44617873 is not prime M44649461 is not prime double-check M45661597 is not prime double-check M45946211 is not prime double-check M46163017 is not prime M46532819 completed P-1 M46804673 is not prime double-check M47075279 is not prime M47285743 is not prime M47297749 is not prime M47478499 is not prime M47577773 is not prime double-check M47618737 is not prime M47651729 is not prime M47795929 is not prime double-check M47950051 is not prime M48022157 is not prime M48090799 is not prime double-check M48559681 is not prime double-check M48955471 is not prime M49144391 is not prime M49168741 is not prime M49362077 is not prime M49769437 is not prime double-check M49871753 is not prime M50201873 is not prime M50368001 is not prime double-check M50386201 is not prime double-check M50489641 is not prime double-check M50559217 is not prime double-check M50565857 is not prime double-check M50622947 is not prime double-check M50856317 is not prime M51278819 is not prime M51352531 is not prime M51529759 is not prime M51597443 is not prime M51663847 is not prime M51900977 is not prime M52356589 is not prime M52795177 is not prime M52800701 is not prime M52895137 is not prime M52963529 is not prime double-check M53038169 is not prime M53205349 is not prime M53441309 is not prime M53972813 is not prime M54041279 is not prime M54044539 is not prime M54137849 is not prime M54174727 is not prime M54558199 is not prime M54679351 is not prime M54755159 is not prime M54757847 is not prime M54982117 is not prime M55053457 is not prime M55106279 is not prime M55156561 is not prime M55190503 is not prime double-check M55233053 is not prime M55261121 is not prime double-check M55291211 is not prime double-check M55311703 is not prime double-check M55349741 is not prime double-check M55354801 is not prime double-check M55540301 is not prime M55638169 is not prime double-check M55665653 is not prime double-check M55930753 is not prime M56168137 is not prime double-check M56221673 is not prime M56255249 is not prime M56462251 is not prime double-check M56538659 is not prime double-check M56627371 is not prime double-check M56651579 is not prime double-check M56803039 is not prime M57024763 is not prime M57151727 is not prime M57173437 is not prime M57175331 is not prime M57400633 is not prime M57753881 is not prime M58022711 is not prime M58285819 is not prime double-check M58411987 is not prime M58437481 is not prime double-check M58465817 is not prime M58521689 is not prime double-check M58586851 is not prime double-check M58634959 is not prime double-check M58695281 is not prime double-check M58763521 is not prime M58813549 is not prime double-check M58884079 is not prime double-check M58968433 is not prime M59010871 is not prime double-check M59053783 is not prime M59082631 is not prime double-check M59187787 is not prime double-check M59239043 is not prime double-check M59239877 is not prime double-check M59257441 is not prime M59260073 is not prime double-check M59273233 is not prime double-check M59287601 is not prime double-check M59368187 is not prime double-check M59505119 is not prime double-check M59561959 is not prime M59576317 is not prime M59723089 is not prime double-check M59957923 is not prime double-check M60181951 is not prime double-check M60497417 is not prime double-check M60576239 is not prime M60688673 is not prime double-check M60848299 is not prime M60911887 is not prime double-check M61042831 is not prime M61057411 is not prime double-check M61179491 is not prime double-check M61260761 is not prime double-check M61320167 is not prime M61354333 is not prime double-check M61446727 is not prime M61469333 is not prime double-check M61525889 is not prime double-check M61549867 is not prime double-check M61551881 is not prime double-check M61569799 is not prime M61598729 is not prime double-check M61622507 is not prime double-check M61667791 is not prime double-check M61705793 is not prime double-check M61739501 is not prime double-check M61784473 is not prime double-check M61801559 is not prime M61831379 is not prime double-check M61873261 is not prime M61887509 is not prime double-check M62031517 is not prime M62108443 is not prime M62801611 is not prime M62834047 is not prime M63131491 is not prime M63151129 is not prime M63274571 is not prime M63467563 is not prime M63644723 is not prime M64155451 is not prime M64166261 is not prime M64414811 is not prime M64455133 is not prime M64599419 is not prime M64734427 is not prime M65167463 is not prime M65309753 is not prime M65743651 is not prime M65952893 is not prime M66256573 is not prime M66652177 is not prime M66726697 is not prime M67093933 is not prime M67221701 is not prime M67335029 is not prime M67749667 is not prime M67915607 is not prime M68163751 is not prime M68941043 is not prime M70384681 is not prime M72181517 is not prime M72291757 is not prime M72601153 is not prime M72754309 is not prime M73150733 is not prime M73151191 is not prime M73210253 is not prime M73475371 is not prime M73502587 is not prime M73564507 is not prime M73816997 is not prime M74007763 is not prime M74076689 is not prime M74486701 is not prime M74830589 is not prime M75492041 is not prime M76521751 is not prime M77270009 is not prime M77494111 is not prime M77918807 is not prime M78217213 is not prime M78294011 is not prime M78466967 is not prime M78723031 is not prime M79147021 is not prime M79426019 is not prime M79473313 is not prime M79639817 is not prime M79813999 is not prime M80146943 is not prime M80546303 is not prime M80659487 is not prime M80870359 is not prime M81003277 is not prime M81772307 is not prime M82053299 is not prime M82560553 is not prime M83062871 is not prime M83631971 is not prime M83917397 is not prime M84228839 is not prime M84420949 is not prime M84482339 is not prime M84541591 is not prime M84650897 is not prime M84984539 is not prime M85483681 is not prime M85769729 is not prime M85912789 completed CERT check M86650079 is not prime M86698253 is not prime M86999551 is not prime M87610441 is not prime M88215031 is not prime M88689319 is not prime M89359943 is not prime M89528731 is not prime M89683777 is not prime M89721271 is not prime M89816257 is not prime M89878351 is not prime M89959183 is not prime M90002041 is not prime M90127343 is not prime M90216527 is not prime M90384059 is not prime M90586099 is not prime M90838273 is not prime M90846953 is not prime M91371871 is not prime M92248549 is not prime M93926467 is not prime M96366511 is not prime M99026593 is not prime M99871363 is not prime M100612703 is not prime M102996457 is not prime M103427581 is not prime M103907707 is not prime M103949129 is not prime M103981727 is not prime M103991233 is not prime M105665003 completed CERT check M105815467 completed P-1 M105936871 is not prime M106253167 completed CERT check M106498061 is not prime M106591627 completed CERT check M106617409 is not prime M106957111 is not prime M107002673 is not prime M107264933 completed CERT check M107358509 completed CERT check M107370037 completed CERT check M107718943 completed CERT check M107778551 is not prime M107814229 is not prime M108007901 completed P-1 M108053497 completed CERT check M108075133 completed CERT check M108077729 completed CERT check M108091309 completed CERT check M108143089 completed CERT check M108250249 completed CERT check M108321113 completed CERT check M108356467 completed CERT check M108610309 completed CERT check M108636149 completed CERT check M108793247 completed CERT check M108917191 is not prime M109012583 completed CERT check M109033979 completed CERT check M109131511 completed CERT check M109269179 completed CERT check M109554089 completed CERT check M109653833 completed CERT check M110015797 completed CERT check M110059247 completed CERT check M110075377 completed CERT check M110242967 completed CERT check M110280491 completed CERT check M110397979 completed CERT check M110445857 completed CERT check M110514743 completed CERT check M110777951 completed CERT check M110868341 completed CERT check M111013787 completed CERT check M111017009 completed CERT check M111090043 completed CERT check M111168121 completed CERT check M111204239 completed CERT check M111207821 completed CERT check M111213017 completed CERT check M111318509 completed CERT check M111383203 completed CERT check M111406859 completed CERT check M111408217 completed P-1 M111542537 completed CERT check M111547067 completed CERT check M111669641 completed CERT check M111751093 completed CERT check M111806237 completed CERT check M111916201 completed P-1 M111935269 completed CERT check M112115467 completed CERT check M112288823 completed P-1 M112321291 completed CERT check M112387721 completed CERT check M112620419 completed P-1 M112955077 completed CERT check M112980671 completed CERT check M112989467 completed CERT check M113345447 completed CERT check M113375021 completed CERT check M113386649 completed P-1 M113921021 completed CERT check M113956489 completed CERT check M114202519 completed CERT check M114376313 completed CERT check M114713353 completed CERT check M114886501 completed CERT check M115575463 completed CERT check M115702471 completed CERT check

[ Stand: 18.12.2022 | Gregor Krannich ]