Sierpinski Number - The Sierpinski Problem

The Sierpinski Problem

The Sierpinski problem is: "What is the smallest Sierpinski number?"

In 1967, Sierpiński and Selfridge conjectured that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem.

To show that 78,557 really is the smallest Sierpinski number, one must show that all the odd numbers smaller than 78,557 are not Sierpinski numbers. That is, for every odd k below 78,557 there exists a positive integer n such that k2n+1 is prime. As of September 2012, there are only six candidates:

k = 10223, 21181, 22699, 24737, 55459, and 67607

which have not been eliminated as possible Sierpinski numbers. Seventeen or Bust (with PrimeGrid), a distributed computing project, is testing these remaining numbers. If the project finds a prime of the form k2n+1 for every remaining k, the Sierpinski problem will be solved.