The Riesel problem

Is \(509203\) the smallest Riesel number — i.e., does every odd \(k < 509203\) admit some \(n\) with \(k\cdot 2^n - 1\) prime?

Riesel (1956) showed \(509203\) admits no prime of the form \(k\cdot 2^n - 1\) and conjectured it minimal. The Riesel problem — eliminate every smaller candidate — became a flagship distributed-computing hunt: Riesel Sieve, then PrimeGrid, grinding through candidates for decades. The search continues; each elimination is a prime found or a covering set proved, and the finish line is a finite check away but not here.