Riesel Problem/Historical Note

Historical Note on Riesel Problem

As of $24$ February $2021$, there remain $48$ values of $k$ below $509 \, 203$ for which no primes have been found of the form:

$k 2^n - 1$

for any positive integer $n$.

They are as follows:

$2293, 9221, 23669, 31859, 38473,$

$46663, 67117, 74699, 81041, 93839,$

$97139, 107347, 121889, 129007, 143047,$

$161669, 192971, 206039, 206231,$

$215443, 226153, 234343, 245561, 250027,$

$315929, 319511, 324011, 325123,$

$327671, 336839, 342847, 344759, 362609,$

$363343, 364903, 365159, 368411, 371893,$

$384539, 386801, 397027, 409753, 444637,$

$470173, 474491, 477583, 485557, 494743$

Any of these may therefore be a Riesel number smaller than $509 \, 203$.

Research is ongoing.