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MathGroup Archive 2001

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[Fwd: [PrimeNumbers] (P-1)/2 also a Prime]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26793] [Fwd: [PrimeNumbers] (P-1)/2 also a Prime]
  • From: Milton Brown <miltbrown at earthlink.net>
  • Date: Wed, 24 Jan 2001 04:18:36 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks for the info.

But, I was not just interested in the Top Ten,
but in generating this type of number randomly
to be used in Cryptology.

It seem that everyone assumes that one is interested
in being on Top.

Milton L. Brown
miltbrown at earthlink.net

Dan Morenus wrote:

> Umm... I believe these are called Sophie Germain primes; for
> the top ten such pairs, ranging from 7075 digits to 18075
> digits, see:
>
> http://www.utm.edu/research/primes/largest.html#Sophie
>
> Proth.exe checks each prime it finds to see if it is a
> Sophie Germain prime.
>
> Milton Brown wrote:
> >
> > The problem is to find primes such that
> > (P-1)/2 is also a prime, useful in Cryptography.
> >
> > Below are some results and the Mathematica
> > statement that does this.
> >
> > Milton L. Brown
> > miltbrown at earthlink.net
> >
> > b =
> > 27891177485678279727891177485678279727891177485678279727891177485678371294\
> >
> > 9895892379294314234990833147;
> >
> > (b-1)/2
> > =139455887428391398639455887428391398639455887428391398639455887428391856474947\
> >
> > 946189647157117495416573
> >
> > c = 3;
> >
> > Do[If[PrimeQ[(c + i - 1)/2] && PrimeQ[c + i],
> >     Print[c + i, " ", (c + i - 1)/2, " ", i]], {i, 2, 1000, 2}]
> > 3 2
> > 5 2
> > 7 3
> > 11 5
> > 23 11
> > 47 23
> > 59 29
> > 83 41
> > 107 53
> > 167 83
> > 179 89
> > 227 113
> > 263 131
> > 347 173
> > 359 179
> > 383 191
> > 467 233
> > 479 239
> > 503 251
> > 563 281
> > 587 359
> > 719 359
> > 839 419
> > 863 431
> > 887 443
> > 983 491
> >
> > Unsubscribe by an email to: primenumbers-unsubscribe at egroups.com
> > The Prime Pages : http://www.primepages.org
>
> -- Dan Morenus (dmorenus at san.rr.com)
>
> --   This parachute is not warranted to be suitable   --
> --    for any purpose, including descending safely    --
> --          from an airplane to the ground.           --


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