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Re: no counter-example???

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  • Adam
    Below is n,k,Q,factorization of Q 11, 4080, 8355841, (13)(41)(61)(257) 11, 4094, 8384513, (277)(30269) 13, 12816, 104988673, (73)(673)(2137) Adam ... prime ...
    Message 1 of 4 , Feb 16, 2008
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      Below is n,k,Q,factorization of Q

      11, 4080, 8355841, (13)(41)(61)(257)
      11, 4094, 8384513, (277)(30269)
      13, 12816, 104988673, (73)(673)(2137)

      Adam

      --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>
      wrote:
      >
      > --- In primenumbers@yahoogroups.com, "Adam" <a_math_guy@> wrote:
      > >
      > > Below I print out prime n, (not required to be prime) k, non-
      prime
      > > value Q, factorization of Q, given that 2^((Q-1)/4) == 1 mod Q.
      > >
      >
      > sorry Adam, I mistated my idea... 2^n+1 <= k <= 2*(2^n+1)
      > now try...
      >
      > > 7, 65, 8321, (53) (157)
      > > 7, 100, 12801, (3) (17) (251)
      > > 11, 170, 348161, (11) (31) (1021)
      > > 11, 1575, 3225601, (71) (181) (251)
      > > 13, 1020, 8355841, (13) (41) (61) (257)
      > > 13, 4917, 40280065, (5) (7) (67) (89) (193)
      > > 17, 801, 104988673, (73) (673) (2137)
      > > 17, 32768, 4294967297, (641) (6700417)
      > > 19, 8192, 4294967297, (641) (6700417)
      > > 19, 101628, 53282340865, (5) (13) (17) (193) (433) (577)
      > > 19, 262145, 137439477761, (593) (231769777)
      > > 23, 512, 4294967297, (641) (6700417)
      > > 29, 8, 4294967297, (641) (6700417)
      > >
      > > Adam
      > >
      > > --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@>
      > > wrote:
      > > >
      > > > not trying to sound like a text book, but...
      > > >
      > > > let Q= k*2^n +1, where 'n'/is prime/ and k<= 2^n +1. I can't
      > find
      > > a
      > > > counter-example... using... if 2^((Q-1)/4) == 1(mod Q), then Q
      is
      > > prime.
      > > >
      > > > I know that using 2 ^ limits the number of psuedo-primes in a
      > search
      > > > Paul Underwood found a C-E when n = 15... but 15 isn't prime.
      > > >
      > >
      >
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