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# The 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.

k Nash weight Contributor Last edit small n next prime
37 630 Riesel Prime Search - 1 2553
337 286 NPLB 2008-09-15 1 11677
1589 396 Karsten Bonath 2007-12-03 4 1620
1721 313 Karsten Bonath 2007-12-03 2 1034
1807 296 Karsten Bonath 2007-12-03 1 1369
2257 501 Karsten Bonath 2007-12-05 1, 5 1297
2317 460 Karsten Bonath 2007-12-22 5 2805
2683 230 David Metcalfe 2007-07-02 7 2239
3775 727 Gary Barnes 2007-07-05 1 1297
5857 541 Gary Barnes 2007-07-05 5 4973
6869 350 Jens Kruse Andersen 2007-10-24 4 45084
10021 513 Karsten Bonath 2011-10-04 3 1835
11887 614 Karsten Bonath 2007-10-24 1, 5 1189
12401 306 Karsten Bonath 2010-07-20 2 26522
17861 271 Karsten Bonath 2007-11-26 2 98954
18089 386 Jens Kruse Andersen 2007-10-24 4 1124
23651 338 (jasong) 2007-10-13 2 237506
24161 230 Jens Kruse Andersen 2007-10-24 2 8570
31453 242 Jens Kruse Andersen 2007-10-24 3 1371
31841 332 Jens Kruse Andersen 2007-10-24 2 1010
32257 367 Jens Kruse Andersen 2007-10-24 1 1985
33373 226 Jens Kruse Andersen 2007-10-24 3 5283
39817 235 Jens Kruse Andersen 2007-10-24 1 1801
43151 556 Jens Kruse Andersen 2007-10-24 2 23286
46411 777 Jens Kruse Andersen 2007-10-24 1 2027
47653 467 Jens Kruse Andersen 2007-10-24 3 1083
55687 429 Jens Kruse Andersen 2007-10-24 1 1597
58331 501 Jens Kruse Andersen 2007-10-24 2 1506
63367 542 Jens Kruse Andersen 2007-10-24 1 1129
67001 291 Jens Kruse Andersen 2007-10-24 2 9506
74857 747 Jens Kruse Andersen 2007-10-24 1 1121
77167 349 (jasong) 2007-10-13 1 153441
79601 766 Jens Kruse Andersen 2007-10-24 2 3542
80771 396 Jens Kruse Andersen 2007-10-24 2 9482
88115 957 Jens Kruse Andersen 2007-10-24 2 2468
90907 317 Jens Kruse Andersen 2007-10-24 1 4689
112391 478 Jens Kruse Andersen 2007-10-24 2 159730
114367 423 Jens Kruse Andersen 2007-10-24 1 1681
115451 409 Jens Kruse Andersen 2007-10-24 2 6218
116257 376 Jens Kruse Andersen 2007-10-24 1 1045
118447 479 Jens Kruse Andersen 2007-10-24 1 14473
120457 619 Jens Kruse Andersen 2007-10-24 1 1261
120997 343 Jens Kruse Andersen 2007-10-24 1 2121
121061 479 Jens Kruse Andersen 2007-10-24 2 2338
122017 582 Jens Kruse Andersen 2007-10-24 1 1257
135787 369 Jens Kruse Andersen 2007-10-24 1 7721
170467 411 Jens Kruse Andersen 2007-10-24 1 55273
173467 408 Jens Kruse Andersen 2007-10-24 1 6925
173587 235 Jens Kruse Andersen 2007-10-24 1 172609
175567 411 CRUS Even Riesel 2023-07-11 1 >10,000,000
179677 625 Jens Kruse Andersen 2007-10-24 1 2729
185347 526 Jens Kruse Andersen 2007-10-24 1 1189
190357 203 Jens Kruse Andersen 2007-10-24 1 15465
190927 518 Jens Kruse Andersen 2007-10-24 1 72289
207397 525 Jens Kruse Andersen 2007-10-24 1 5609
209737 406 Jens Kruse Andersen 2007-10-24 1 1313
230407 291 Jens Kruse Andersen 2007-10-24 1 1105
230827 495 Jens Kruse Andersen 2007-10-24 1 4177
233221 618 Jens Kruse Andersen 2007-10-24 1 1021
239107 153 CRUS Even Riesel 2023-07-11 1 >10,000,000
246787 219 Jens Kruse Andersen 2007-10-24 1 1081

## Status

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

Riesel primes
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