# Riesel problem

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The **Riesel problem** consists in determining the smallest Riesel number.

In 1956, Hans Riesel showed that there are an infinite number of integers *k* such that *k × 2 ^{n} − 1* is not prime for any integer

*n*. He showed that the number

*k = 509,203*has this property. It is conjectured that 509203 is the smallest such number that has this property. To prove this, it suffices to show that there exists a value

*n*such that

*k × 2*is prime for each k ≤ 509202. As of Aug. 2019, there are 49 k values smaller than 509203 that have no known primes.

^{n}- 1