Proth prime

A Proth prime is not a true class of numbers, but primes in the form k•2ⁿ+1 with 2ⁿ > k are often called Proth primes.

Different from this definition all values n ≥ 1 are listed in Prime-Wiki.

See Also

• The PSearch Project
• Proth's theorem
• Table with all available k-values

External Links

• Definition from The Prime Glossary
• Definition from MathWorld
• Wikipedia

Proth primes

Miscellaneous

Proth prime Sierpiński problem Least n (k≤12)

Tables

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Categories

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Others

3k 15k 2145k 2805k 0 primes 100+ primes Sierpiński numbers Missing ranges

Other categories

Sierpiński numbers Missing ranges Low weight Count 0

Other bases

3 4 5 6 7 11 999

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