Provable Riesel numbers (A076337).

[David Wilson]

I agree that "Proven Sierpinski (Riesel) number" is superior to
"Provable Sierpinski (Riesel) number".  How about

Aside: Wasn't there a discussion in seqfan/math-fun about the
past participle of "prove"?  I remember hearing that "proved"
means "demonstrated" while "proven" means "field tested", in
which case we would say "Proved Sierpinski (Riesel) numbers".
Given the state of modern English, this is a nit-pick though.

How about this:

%N A076336 Proven Sierpinski numbers: n such that n*2^k+1 has
been shown composite for all k >= 1.
%C A076336 Sierpinski numbers are proved by exhibiting a periodic
sequence p of prime divisors with p(k) | n*2^k+1, and disproved
by finding prime n*2^k+1.  It is conjectured that numbers that
cannot be proved Sierpinski in this way are non-Sierpinski.
However, some numbers resist both proof and disproof.

%N A076337 Proven Riesel numbers: n such that n*2^k-1 has been
shown composite for all k >= 1.
%C A076337 Riesel numbers are proved by exhibiting a periodic
sequence p of prime divisors with p(k) | n*2^k-1, and disproved
by finding prime n*2^k-1.  It is conjectured that numbers that
cannot be proved Riesel in this way are non-Riesel. However, some
numbers resist both proof and disproof.