Riesel number

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A Riesel number is a value of k such that k•2ⁿ-1 is always composite for all natural numbers.

Using the same method presented in the Sierpiński problem article, Hans Riesel found in 1956 that 509203•2ⁿ-1 is always composite.

In order to demonstrate whether 509203 is the smallest Riesel number or not (the Riesel problem), a distributed computing project was created named Riesel Sieve.

See also

• Riesel and Proth Prime Database
• Riesel problem
• Riesel prime
• 15,000 Riesel numbers in the sequence A101036 in OEIS
• Category: Riesel numbers

External links

• MathWorld
• Riesel number

Number classes

General numbers

Integer Natural Even Odd Rational Irrational Real Prime Probable prime

Special numbers

Mersenne 2n-1 Fermat 22n+1 Proth k•2n+1 Riesel k•2n-1 Woodall n•2n-1 Cullen n•2n+1 Double Mersenne 22p-1-1 Perfect 2n-1(2n-1) Leyland xy ± yx Gen.Repunit (b^n-1)/(b-1)

Prime numbers

Mersenne Proth Riesel Williams (b±1)bn±1 Carol/Kynea (bn±1)2-2 Multifactorial n!j±1