Even Riesel Problem

Overview

The Riesel problem is to find the smallest Riesel number k (odd) such that k•2ⁿ-1 is composite for every n ≥ 1.

This page was inspired by two threads of the MersenneForum here and here started by (jasong).

Except a few numbers of the odd k's of the Riesel problem a prime was found (mostly a higher n). But what about k's with only a prime with very low n, say n = 1?

For example: k = 17861 is prime for n = 2 and no other n < 50000. So the even value k = 17861 • 2 • 2 = 71444 has no prime for n < 49998.

Accordingly there comes up a question: Is there any even k for which k • 2n − 1 is never prime?

Data

The table contains all 61 odd k < 254601 which got only small prime(s) for n < 10 and no other for n < 1000. 9 candidates of them got no other prime for n < 50000. These computations were made by Jens K. Andersen and (jasong) in Oct 2007.

(Table missing.)

Status

Only 2 of these 61 candidates got no higher prime n: k = 175567 and k = 239107 (see the Even Riesel project).

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