Riesel Problem

From ProofWiki
Jump to navigation Jump to search

Unsolved Problem

What is the smallest Riesel number?


Source of Name

This entry was named for Hans Ivar Riesel.


Historical Note

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.


Sources