Projekt GIMPS (Great Internet Mersenne Prime Search)

GIMPS Logo


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:

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).


Icon für 2 hoch n - 1   Die folgenden 1125 Exponenten haben meine Rechner bisher getestet (das M steht für Mersenne-Exponent):

   M190529 completed CERT check
   M190579 completed CERT check
   M190613 completed CERT check
   M190639 completed CERT check
   M190649 completed CERT check
   M237409 completed CERT check
   M326063 completed CERT check
   M363551 completed CERT check
   M363557 completed CERT check
   M385621 completed CERT check
   M386437 completed CERT check
   M386471 completed CERT check
   M391739 completed CERT check
   M397283 completed CERT check
  M1157699 completed CERT check
  M1161059 completed CERT check
  M1177019 completed CERT check
  M1974851 completed CERT check
  M2177093 completed CERT check
  M2216281 completed CERT check
  M2242843 completed CERT check
  M2264183 completed CERT check
  M2278021 completed CERT check
  M2522087 completed CERT check
  M2632793 completed CERT check
  M2763967 completed CERT check
  M2824123 completed CERT check
  M3841141 completed CERT check
  M4317409 completed CERT check
  M4395887 completed CERT check
  M4470803 completed CERT check
  M5136013 completed CERT check
  M5538167 completed CERT check
  M5655619 completed CERT check
  M6535673 is not prime
  M6724951 completed CERT check
  M6810019 completed CERT check
  M6882641 completed CERT check
  M6883091 completed CERT check
  M7645951 completed CERT check
  M7930003 completed CERT check
  M7993211 completed CERT check
  M8074309 completed CERT check
  M8225573 completed CERT check
  M8269691 is not prime
  M8444609 completed CERT check
  M8551733 is not prime
  M8711669 is not prime
  M8713631 is not prime
  M8789747 completed CERT check
  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
 M10134307 completed CERT check
 M10168987 completed CERT check
 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
 M11059141 completed CERT check
 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
 M13691719 completed CERT check
 M13747879 is not prime
 M13755769 completed CERT check
 M13756807 completed CERT check
 M13802951 completed CERT check
 M13817191 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
 M14915333 completed CERT check
 M14998531 completed CERT check
 M15213287 is not prime
 M15354037 completed CERT check
 M15395033 is not prime
 M15496849 completed CERT check
 M15497507 completed CERT check
 M15546847 is not prime
 M15675859 completed CERT check
 M15709961 completed CERT check
 M15710689 completed CERT check
 M15729943 completed CERT check
 M15756379 completed CERT check
 M15795799 completed CERT check
 M15801319 is not prime
 M15804589 completed CERT check
 M15811357 completed CERT check
 M15813437 completed CERT check
 M15827507 completed CERT check
 M15839231 completed CERT check
 M15846829 completed CERT check
 M15862849 completed CERT check
 M15871501 completed CERT check
 M15878059 is not prime
 M15948209 completed CERT check
 M15954227 completed CERT check
 M15957803 completed CERT check
 M15959473 completed CERT check
 M15965311 is not prime
 M15966169 completed CERT check
 M15972041 completed CERT check
 M15981419 completed CERT check
 M15984707 completed CERT check
 M16007419 completed CERT check
 M16009211 completed CERT check
 M16009241 completed CERT check
 M16009963 completed CERT check
 M16030153 completed CERT check
 M16032767 completed CERT check
 M16033609 completed CERT check
 M16040837 completed CERT check
 M16049647 completed CERT check
 M16063511 completed CERT check
 M16064803 completed CERT check
 M16064831 completed CERT check
 M16068347 completed CERT check
 M16069853 completed CERT check
 M16091497 completed CERT check
 M16098659 completed CERT check
 M16103293 completed CERT check
 M16106483 completed CERT check
 M16138169 completed CERT check
 M16142293 completed CERT check
 M16146269 completed CERT check
 M16149521 completed CERT check
 M16150609 is not prime
 M16152379 completed CERT check
 M16158277 completed CERT check
 M16161553 completed CERT check
 M16168261 completed CERT check
 M16175813 completed CERT check
 M16202551 completed CERT check
 M16216477 completed CERT check
 M16217449 completed CERT check
 M16218907 completed CERT check
 M16227611 completed CERT check
 M16230661 completed CERT check
 M16231687 completed CERT check
 M16231711 completed CERT check
 M16235147 completed CERT check
 M16235249 completed CERT check
 M16235449 completed CERT check
 M16269431 completed CERT check
 M16278679 completed CERT check
 M16286027 completed CERT check
 M16292317 completed CERT check
 M16295921 completed CERT check
 M16301533 completed CERT check
 M16305733 completed CERT check
 M16316171 completed CERT check
 M16319003 completed CERT check
 M16324739 completed CERT check
 M16328969 completed CERT check
 M16335733 completed CERT check
 M16337957 completed CERT check
 M16343843 completed CERT check
 M16355557 completed CERT check
 M16357951 completed CERT check
 M16358891 completed CERT check
 M16377457 completed CERT check
 M16402697 completed CERT check
 M16407103 completed CERT check
 M16414547 completed CERT check
 M16588633 is not prime
 M16614041 completed CERT check
 M16624661 is not prime
 M16664261 completed CERT check
 M16678483 completed CERT check
 M16684099 completed CERT check
 M16693889 completed CERT check
 M16861217 completed CERT check
 M16869829 completed CERT check
 M16883903 is not prime
 M16899041 is not prime
 M16920107 is not prime
 M16935241 completed CERT check
 M17000479 completed CERT check
 M17015729 completed CERT check
 M17036233 is not prime
 M17138917 is not prime
 M17272237 completed CERT check
 M17282563 is not prime
 M17334949 completed CERT check
 M17510371 is not prime
 M17564681 is not prime
 M17609587 completed CERT check
 M17702803 completed CERT check
 M17702843 completed CERT check
 M17711143 has a factor: 11811068152556338975780399
 M17763349 completed CERT check
 M18000869 completed CERT check
 M21092647 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
 M62176181 completed CERT check
 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
 M64999537 completed CERT check
 M65167463 is not prime
 M65309753 is not prime
 M65743651 is not prime
 M65952893 is not prime
 M66003467 is not prime
 M66256573 is not prime
 M66380893 is not prime
 M66565259 completed CERT check
 M66652177 is not prime
 M66726697 is not prime
 M66897539 is not prime
 M66996067 is not prime
 M67093933 is not prime
 M67221701 is not prime
 M67335029 is not prime
 M67479757 completed CERT check
 M67536419 is not prime
 M67720087 is not prime
 M67749667 is not prime
 M67915607 is not prime
 M68163751 is not prime
 M68434649 is not prime
 M68749081 is not prime
 M68802659 completed CERT check
 M68941043 is not prime
 M69024457 completed CERT check
 M69289853 is not prime
 M69590413 is not prime
 M69623107 is not prime
 M69720347 is not prime
 M69809653 is not prime
 M69827627 is not prime
 M70384681 is not prime
 M70410953 completed CERT check
 M70679927 is not prime
 M70721797 is not prime
 M71097907 completed CERT check
 M71115509 completed CERT check
 M71123531 completed CERT check
 M71132249 completed CERT check
 M71228659 is not prime
 M71238173 is not prime
 M71401181 completed CERT check
 M71540221 completed CERT check
 M72181517 is not prime
 M72291757 is not prime
 M72601153 is not prime
 M72667303 completed CERT check
 M72754309 is not prime
 M73042577 completed CERT check
 M73150733 is not prime
 M73151191 is not prime
 M73210253 is not prime
 M73409339 completed CERT check
 M73475371 is not prime
 M73502587 is not prime
 M73510027 completed CERT check
 M73564507 is not prime
 M73670123 is not prime
 M73814263 completed CERT check
 M73816997 is not prime
 M74007763 is not prime
 M74076689 is not prime
 M74410223 is not prime
 M74484073 completed CERT check
 M74486701 is not prime
 M74713217 completed CERT check
 M74830589 is not prime
 M75317947 completed CERT check
 M75492041 is not prime
 M75928663 completed CERT check
 M76332343 completed CERT check
 M76521751 is not prime
 M76642421 completed CERT check
 M76937701 completed CERT check
 M77147597 completed CERT check
 M77217403 completed CERT check
 M77270009 is not prime
 M77494111 is not prime
 M77918807 is not prime
 M78217213 is not prime
 M78294011 is not prime
 M78466967 is not prime
 M78594097 completed CERT check
 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
 M82649921 completed CERT check
 M82695359 completed CERT check
 M82775003 completed CERT check
 M82776119 completed CERT check
 M82904483 completed CERT check
 M82904519 completed CERT check
 M82993049 completed CERT check
 M83062871 is not prime
 M83143757 completed CERT check
 M83161231 completed CERT check
 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
 M85491337 completed CERT check
 M85734427 completed CERT check
 M85769729 is not prime
 M85774001 completed CERT check
 M85912789 completed CERT check
 M86106247 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
 M89661763 completed CERT check
 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
 M91265093 completed CERT check
 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
M106875193 completed CERT check
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
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[ Stand: 08.03.2025 | Email IconGregor Krannich ]