Projekt GIMPS (Great Internet Mersenne Prime Search)

GIMPS Logo


Seit Mai 2011 rechnet mein Intel(R) Core(TM) i3-2100T (SandyBridge) an den Primzahlen. Dieser löste den mittlerweile betagten Computer AMD Athlon(TM) 64 X2 Dual Core Processor 3800+ ab und ich spare ca. 600kWh Strom im Jahr! Bis Januar 2007 rechnete ein Intel(R) Pentium(TM) II 450 MHz mit 2 Prozessoren. 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.

Privat erschwingliche Computer sind mittlerweile in dem Bereich der Rechenleistung, der nötig ist, um Zahlen mit etwa 10 Mio Stellen in verhältnismäßig kurzer Zeit testen zu können. Um eine solche Zahl zu testen, ob sie prim ist oder nicht, benötigt ein aktueller Prozessor mit 3GHz etwa 1,5 Monate Rechenzeit. Die heute üblichen Quad-Core, Hexa-Core, Octa-Core oder 12-Core CPUs verkürzen die Rechenzeit für einen Einzeltest nicht, aber man kann parallel mehrere Zahlen testen. Bis eine Primzahl mit mehr als 100 Mio Stellen gefunden wird, wird es sicher wieder mehr als 10 Jahre dauern.

Bevor ein Lucas-Lehmer-Test ausgefürt wird, wird zunächst geprüft, ob es Faktoren gibt, die kleiner als 2^68 sind. Manchmal werden welche gefunden, diese sind in der nachfolgenden Liste mit dabei.
Icon für 2 hoch n - 1   Die folgenden 294 Exponenten haben meine Rechner bisher getestet (das M steht für Mersenne-Exponent):


 M6535673 is not prime
 M8269691 is not prime
 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
 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
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
M11667683 is not prime
M11790991 is not prime
M11884267 is not prime
M11972159 is not prime
M12058357 is not prime
M12165787 is not prime
M12173237 is not prime
M12230221 is not prime
M12280687 is not prime
M12374737 is not prime
M12434483 is not prime
M12524177 is not prime
M12593681 is not prime
M12635251 is not prime
M12847349 is not prime
M12930067 is not prime
M13099717 is not prime
M13147327 is not prime
M13206257 is not prime
M13239469 is not prime
M13382459 is not prime
M13541417 is not prime
M13747879 is not prime
M13875677 is not prime
M13958333 is not prime
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
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
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
M24647813 is not prime
M24809621 is not prime
M24865703 is not prime
M24872191 is not prime
M24878551 is not prime
M25150663 is not prime
M25198933 is not prime
M25304233 is not prime
M25340267 is not prime
M25455217 is not prime
M25654963 is not prime
M25833007 is not prime
M26148643 is not prime
M26283079 is not prime
M26374987 is not prime
M26436721 is not prime
M26848769 is not prime
M26869897 is not prime
M27153211 is not prime
M27439793 is not prime
M27540859 is not prime
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
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
M41660159 is not prime
M41661811 has a factor: 648777276331488364129
M41796449 is not prime
M41986793 is not prime
M42508859 is not prime
M42735089 is not prime
M43171159 is not prime
M43196389 is not prime
M44282531 is not prime
M44335619 is not prime
M44403497 is not prime
M44563327 is not prime
M44617873 is not prime
M46163017 is not prime
M47075279 is not prime
M47285743 is not prime
M47297749 is not prime
M47478499 is not prime
M47618737 is not prime
M47651729 is not prime
M47950051 is not prime
M48022157 is not prime
M48955471 is not prime
M49144391 is not prime
M49168741 is not prime
M49362077 is not prime
M49871753 is not prime
M50201873 is not prime
M50622947 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
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
M55233053 is not prime
M55540301 is not prime
M55930753 is not prime
M56221673 is not prime
M56255249 is not prime
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
M58411987 is not prime
M58465817 is not prime
M58763521 is not prime
M58968433 is not prime
M59053783 is not prime
M59257441 is not prime
M59561959 is not prime
M59576317 is not prime
M60576239 is not prime
M60848299 is not prime
M61042831 is not prime
M61320167 is not prime
M61446727 is not prime
M61569799 is not prime
M61801559 is not prime
M61873261 is not prime
M62031517 is not prime
M62108443 is not prime
M62801611 is not prime
M62834047 is not prime
M63131491 is not prime
M63274571 is not prime
M63467563 is not prime
M63644723 is not prime
M64155451 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





[ Stand: 29.10.2017 | Email IconGregor Krannich ]