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 × 2n − 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 × 2n - 1 is prime for each k ≤ 509202. As of Aug. 2019, there are 49 k values smaller than 509203 that have no known primes.

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