Re: [PrimeNumbers] Re: Primes with the representation of the year in them
- --- On Fri, 11/25/11, djbroadhurst <d.broadhurst@...> wrote:
> Phil Carmody <thefatphil@...> wrote:Yeah, I'm clearly confused. This happens occasionally.
> > I see no reason why larger p wouldn't permit us to cover
> > everything divisible by 2011 with other primes
> The concept of a covering set is familiar in the context of
> (n^q + c)/d, with (n, c, d) held fixed, but not (to me at least)
> in the present context, with (q = p^p, c = 2, d = 2011) held fixed
> and only the base, n, allowed to vary.
> > I would expect it to be quite easy to arrive at a 0 answer.
> I am unable to do so except in the trivial cases p = 3 and
> p = 67.
> On the contrary, I conjecture that for every prime p that does not
> divide znorder(Mod(-2,2011)) = 3*67 there is an infinitude
> of primes
> of the form (n^(p^p)+2)/2011, with fixed p, even though we
> presently know of no probable prime in any case with p > 5.