Sierpinskin luku Sisällysluettelo Sierpinskin ongelma | Katso myös | Lähteet | Aiheesta muualla | NavigointivalikkoSeventeen or Bust: Project statsSeventeen or Bustlaajentamalla

LukuteoriaRatkaisemattomat matemaattiset ongelmat


Lukuteoriassaparitontaluonnollista lukuakokonaisluvutyhdistettyjä lukujaalkulukujaProthin luvuiksi1960Wacław Sierpiński1962John SelfridgeSeventeen or Bust





Lukuteoriassa Sierpinskin luku tarkoittaa sellaista paritonta luonnollista lukua k, jolle pätee, että kaikki kokonaisluvut muotoa k × 2n + 1 ovat yhdistettyjä lukuja (siis eivät ole alkulukuja) kaikilla n:n arvoilla.


Toisin sanoen k:n ollessa Sierpinskin luku kaikki joukon


k⋅2n+1:n∈Ndisplaystyle left,kcdot 2^n+1:nin mathbb N ,right

alkiot ovat yhdistettyjä lukuja. Joukon lukuja, kun k on pariton ja k<2ndisplaystyle k<2^n, kutsutaan Prothin luvuiksi.


Vuonna 1960 Wacław Sierpiński, jonka mukaan Sierpinskin luku on nimetty, todisti, että on olemassa äärettömän monta paritonta kokonaislukua k, jotka eivät tuota alkulukuja.




Sisällysluettelo





  • 1 Sierpinskin ongelma


  • 2 Katso myös


  • 3 Lähteet


  • 4 Aiheesta muualla




Sierpinskin ongelma |


Sierpinskin ongelma kysyy, mikä on pienin Sierpinskin luku. Vuonna 1962[1]John Selfridge todisti, että 78 557 on Sierpinskin luku. Hän julkisti (mutta ei todistanut) Selfridgen konjektuurin, jonka mukaan 78 557 olisi pienin Sierpinskin luku ja siten siis vastaus Sierpinskin ongelmaan. Internetissä toimiva hajautetun laskennan projekti Seventeen or Bust etsii pienintä mahdollista Sierpinskin lukua ja pyrkii todistamaan Sierpinskin ongelmaa. Lokakuussa 2009 on jäljellä enää kuusi ehdokasta mahdollisiksi 78 557:ää pienemmiksi Sierpinskin luvuiksi: 10 223, 21 181, 22 699, 24 737, 55 459 ja 67 607.[2]



Katso myös |


  • Brierin luku


Lähteet |



  1. ↑ bit.ly/Xt3S9Y John Selfridge


  2. ↑ Seventeen or Bust: Project stats



Aiheesta muualla |


  • Seventeen or Bust

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