Proth number

In number theory, a Proth number is a number of the form

N = k × 2ⁿ + 1

where k is an odd positive integer and n is a positive integer such that 2ⁿ > k.

Without the condition that 2ⁿ > k, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too.

A Proth prime is a Proth number, which is prime.

Cullen numbers (n × 2ⁿ+1) and Fermat numbers (2²ⁿ+1) are special forms of Proth numbers.

See also

• Riesel number

External links

• Proth 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