Riesel Problem
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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.