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Re: [PrimeNumbers] Wonderful primes generator(s)

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  • Jens Kruse Andersen
    ... = 2^(n-3)*(2^3 + 2^2 + 2^1 + 1) +/- 1 = 2^(n-3)*15 +/- 1 = 15*2^m +/- 1, for m=n-3 and m 0. ... rank description digits who year
    Message 1 of 2 , Nov 13, 2004
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      Peter Lesala wrote:

      > 2^n + 2^(n - 1) + 2^(n - 2) + 2^(n - 3)+/- 1, for n => 4

      = 2^(n-3)*(2^3 + 2^2 + 2^1 + 1) +/- 1 = 2^(n-3)*15 +/- 1
      = 15*2^m +/- 1, for m=n-3 and m>0.

      From http://primes.utm.edu/primes/search.php :
      ----- -------------------------------- ------- ---- ---- --------------
      rank description digits who year
      ----- -------------------------------- ------- ---- ---- --------------
      99 15*2^734400+1 221078 p76 2004
      108 15*2^701902+1 211295 p76 2004
      162 15*2^635989+1 191453 p76 2004
      232 15*2^483098+1 145429 p76 2004
      252 15*2^454681-1 136874 L52 2004
      339 15*2^403929+1 121596 p114 2002
      1012 15*2^300488+1 90458 p114 2002
      1044 15*2^294894+1 88774 p76 2003
      3744 15*2^184290+1 55478 Y 1998
      5182 15*2^172714-1 51994 L52 2004
      6817 15*2^161453-1 48604 L52 2004
      10589 15*2^115327-1 34719 L1 2003
      15066 15*2^91457-1 27533 g138 1999
      15948 15*2^83669-1 25189 g138 1999
      15977 15*2^83263-1 25066 g138 1999
      19171 15*2^61758+1 18593 Y 1995
      19372 15*2^60622-1 18251 g138 1999
      22188 15*2^48444+1 14585 Y 1995
      23798 15*2^43388+1 13063 Y 1995
      24663 15*2^41054-1 12360 g138 1999
      24735 15*2^40742-1 12266 g138 1999
      26521 15*2^34260+1 10315 D 1993
      26530 15*2^34224+1 10304 D 1993
      29510 15*2^24995+1 7526 D 1993
      29868 15*2^24105+1 7258 D 1993
      31165 15*2^21962-1 6613 gk 1998
      31230 15*2^21727-1 6542 gk 1998
      31351 15*2^21550+1 6489 D 1993
      31380 15*2^21445+1 6457 D 1992
      32447 15*2^19219+1 5787 D 1992
      42088 15*2^7613-1 2293 D 1994
      42533 15*2^7392+1 2227 K 1983
      43446 15*2^7050+1 2124 K 1983
      44318 15*2^6804+1 2050 K 1983
      51180 15*2^4410+1 1329 K 1983
      57983 15*2^3888+1 1172 CW 1979

      --
      Jens Kruse Andersen
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