Re: n odd, when is n +/- 2^x prime?
- 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
--- In email@example.com, "jbrennen" <jb@b...> wrote:
> --- In firstname.lastname@example.org, Mark Underwood wrote:
> > Perhaps - egad - there exist a first n such that n +/- 2^x is
> > prime? I doubt that last one, but who knows...
> I'm not claiming it's the first n, but one such n would be:
> 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: