Gigantiska primtal

Gigantiska primtal betecknar primtal med åtminstone 10 000 siffror. Begreppet dök första gången upp i Journal of Recreational Mathematics i artikeln “Collecting gigantic and titanic primes” (1992) av Samuel Yates.

Chris Caldwell som har fortsatt på Yates samling av primtal har berättat att han ändrade det ursprungliga kravet på 5 000 siffror till 10 000, när han ombads att revidera artikeln efter Yates död.[1] Då var inte många sådana primtal kända, men för dagens datorer är beräkningen snabb, varför många kan finnas på en enda dag.[2][3]

Det först upptäckta gigantiska primtalet var Mersenneprimtalet 244497 − 1. Det har 13 395 siffror och hittades 1979 av den amerikanske matematikern och dataprogrammeraren Harry Lewis Nelson och matematikern vid Cray, Inc. David Slowinski. [4]

Det minsta gigantiska primtalet är 109999 + 33603. Det bevisades vara primtal 2003 av de tyska matematikerna Jens Franke, Thorsten Kleinjung och Tobias Wirth med deras eget datorprogram ECPP (Elliptic curve primality proving).

Se även

Referenser

  1. ^ Caldwell, Chris K. (22 november 1992). ”The Prime Pages – Yater 92b”. The University of Tennessee at Martin. http://primes.utm.edu/references/refs.cgi?long=Yates92b. Läst 4 november 2013. 
  2. ^ Eva-Lotta Högberg, Daniel Norin, Linn Stengård, Joakim Widén (22 november 2002). ”Numerisk talteori”. Uppsala Universitet. http://www.it.uu.se/edu/course/homepage/numSTS1/redovisningar/historiska_moment/Grupp_1_Talteori.pdf. Läst 4 november 2013. 
  3. ^ ”How to find a giant prime number”. Crosci – Croatian Science Portal. 22 november 2013. Arkiverad från originalet den 5 november 2013. https://web.archive.org/web/20131105061714/http://crosci.com/how-to-find-a-giant-prime-number.html. Läst 4 november 2013. 
  4. ^ ”The Largest Known Prime by Year: A Brief History”. University of Tennessee at Martin. http://primes.utm.edu/notes/by_year.html. Läst 4 november 2013. 

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