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Re: n odd, when is n +/- 2^x prime?

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  • Mark Underwood
    Well I am in awe, thank you Jack. Brier numbers are such that both n*2^k + 1 and n*2^k - 1 are always composite for certain n and any k, but Jack is saying
    Message 1 of 3 , Dec 29, 2005
      Well I am in awe, thank you Jack. Brier numbers are such that both
      n*2^k + 1 and n*2^k - 1 are always composite for certain n and any k,
      but Jack is saying that this applies also, for the same n, to n + 2^k
      and n - 2^k !

      I've checked Jack's number n = 878503122374924101526292469
      and it is indeed composite for n +/- 2^k ,at least up to exponent k =
      3000. But I can't figure out how the primelessness of n*2^k +/- 1 is
      related to the primelessness of n +/- 2^k for the same n. If this is
      elementary, I would appreciate any insight that anyone can offer into
      this, thanks.

      Mark



      --- In primenumbers@yahoogroups.com, "jbrennen" <jb@b...> wrote:
      >
      > --- In primenumbers@yahoogroups.com, Mark Underwood wrote:
      > > Perhaps - egad - there exist a first n such that n +/- 2^x is
      *never*
      > > prime? I doubt that last one, but who knows...
      >
      > I'm not claiming it's the first n, but one such n would be:
      >
      > 1401087257
      >
      > Generally, almost any Sierpinski number will satisfy that n+2^x
      > is never prime, and it's likely that an infinite number of them
      > also satisfy n-2^x is never prime. Note that I'm assuming that
      > once 2^x exceeds n, you stop checking n-2^x -- i.e., negative
      > numbers don't count as primes.
      >
      > If negative numbers do count as primes, you need to look at
      > "Brier numbers" -- numbers which are simultaneously Sierpinski
      > numbers and Riesel numbers. According to the OEIS, the smallest
      > known Brier number has 27 digits:
      >
      > 878503122374924101526292469
      >
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