Projekt GIMPS (Great Internet Mersenne Prime Search)

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 Dual- oder Quad-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.

Die folgenden 181 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
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
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
M42508859 is not prime
M42735089 is not prime
M43171159 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
M47478499 is not prime
M47618737 is not prime
M47651729 is not prime
M47950051 is not prime
M48022157 is not prime
M48955471 is not prime
M49168741 is not prime
M50201873 is not prime
M50622947 is not prime
M51278819 is not prime
M51529759 is not prime
M51597443 is not prime
M52800701 is not prime
M53205349 is not prime
M53441309 is not prime
M53972813 is not prime
M54041279 is not prime
M54174727 is not prime
M54679351 is not prime
M55930753 is not prime

[ Stand: 21.01.2012 |

Gregor Krannich ]