Riesel prime

Although there's no official definition of a Riesel prime mostly all primes of the form k•2ⁿ-1 with 2ⁿ > k are called like this on many pages.

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

Sources

Threads from MersenneForum:

Ongoing

• "RPS k*2^n-1, k<300 reservations/status": #1 (2007-07-08) - #1087 (2024-08-16)
• "Post top-5000 primes here": #1 (2010-03-17) - #1986 (2024-05-22)
• "Team drive #1 for k<300: many k's for n=2M-3M": #1 (2024-04-23) - (ongoing)

Terminated

• "k=4001-4199": #1 (2016-02-11) - #7 (2020-03-27)
• "Individual-k reservations k=300-400 n=600K-1M": #1 (2008-04-02) - #404 (2010-02-28)
• "Team drives #15-16; k=300-400 n=2M-3M; Individual reservations k=310-350": #1 (2010-03-21) - #280 (2023-03-08)

Others

• IDs and found dates from the The Prime Pages

See also

• Riesel and Proth Prime Database

External links

• Riesel number
• Proth Search page

Riesel primes

Base = 2 :

Miscellaneous

Riesel prime Riesel problem 1 Riesel problem 2 Riesel problem 3 Riesel problem 4 Riesel numbers 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 Riesel numbers Missing ranges

Other categories

Missing ranges Low weight No Sophie Germain No twin Count 0 Constant n

Other bases

3 4 5 10 16 128 263 284

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