A positive number `k` is a Sierpinski number if there
are no primes of the form
`k`^{.}2^{n}+1 for any positive
number `n` (for `k` < 2^{n}).

Primes of this form are called Proth primes, they are relatively
easy to prove prime because of Proth's Theorem. It is much harder to
prove that a number is a Sierpinski number.

The lowest known Sierpinski number is 78557. The Sierpinski
conjecture states that this is the lowest Sierpinski number, but this
remains unproven.