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• ... sorry Adam, I mistated my idea... 2^n+1
Message 1 of 4 , Feb 15, 2008
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>
> 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)
>
>
> --- 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.
> >
>
• 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)

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)
> >
> >
> > --- 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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