The even Riesel-Problem

Overview:

The Riesel Problem (see here) 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 forum 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.

Status :

Only 2 of these 61 candidates got no higher prime n: k = 175567 and 239107.

kNash
weight		contributorlast editsearch
limit n		small n
prime(s)		next
prime n		more prime n
37 630 G.Barnes - 1.0M 1 2553 4893, 7897, 14353, 32125, 51477, 78973, 341365
337 286 NPLB 2008-09-15 1.0M 1 11677 12101, 44149, 72997, 147929, 171509
1589 396 K.Bonath 2007-12-03 100k 4 1620 15480, 28444
1721 313 K.Bonath 2007-12-03 100k 2 1034 9818, 75818, (...) 413634
1807 296 K.Bonath 2007-12-03 100k 1 1369 -
2257 501 K.Bonath 2007-12-05 350k 1, 5 1297 5345, 11393, 20333, 44513, 66893
2317 460 K.Bonath 2007-12-22 350k 5 2805 4345, 14657, 17017
2683 230 D.Metcalfe 2007-07-02 1.2M 7 2239 -
3775 727 G.Barnes 2007-07-05 10k 1 1297 -
5857 541 G.Barnes 2007-07-05 10k 5 4973 5909
6869 350 J.K.Andersen 2007-10-24 45k 4 45084 -
10021 513 K.Bonath 2011-10-04 1.301M 3 1835 27083, 77673, 78611, 90561, 396723, 1033905, 1119611
11887 614 K.Bonath 2007-10-24 100k 1, 5 1189 6937, 14185, 26125, 53989
12401 306 K.Bonath 2010-07-20 1.0M 2 26522 58226, 595154, 773054
17861 271 K.Bonath 2007-11-26 294k 2 98954 256010
18089 386 J.K.Andersen 2007-10-24 1,1k 4 1124 -
23651 338 (jasong) 2007-10-13 237k 2 237506 -
24161 230 J.K.Andersen 2007-10-24 8.5k 2 8570 -
31453 242 J.K.Andersen 2007-10-24 1.3k 3 1371 -
31841 332 J.K.Andersen 2007-10-24 1k 2 1010 -
32257 367 J.K.Andersen 2007-10-24 1.9k 1 1985 -
33373 226 J.K.Andersen 2007-10-24 5.2k 3 5283 -
39817 235 J.K.Andersen 2007-10-24 1.8k 1 1801 -
43151 556 J.K.Andersen 2007-10-24 23.2k 2 23286 -
46411 777 J.K.Andersen 2007-10-24 2k 1 2027 -
47653 467 J.K.Andersen 2007-10-24 1k 3 1083 -
55687 429 J.K.Andersen 2007-10-24 1.5k 1 1597 -
58331 501 J.K.Andersen 2007-10-24 1.5k 2 1506 -
63367 542 J.K.Andersen 2007-10-24 1k 1 1129 -
67001 291 J.K.Andersen 2007-10-24 9.5k 2 9506 -
74857 747 J.K.Andersen 2007-10-24 1k 1 1121 -
77167 349 (jasong) 2007-10-13 153k 1 153441 -
79601 766 J.K.Andersen 2007-10-24 3.5k 2 3542 -
80771 396 J.K.Andersen 2007-10-24 9.4k 2 9482 -
88115 957 J.K.Andersen 2007-10-24 2.4k 2 2468 -
90907 317 J.K.Andersen 2007-10-24 4.6k 1 4689 -
112391 478 J.K.Andersen 2007-10-24 159k 2 159730 -
114367 423 J.K.Andersen 2007-10-24 1.6k 1 1681 -
115451 409 J.K.Andersen 2007-10-24 6.2k 2 6218 -
116257 376 J.K.Andersen 2007-10-24 1k 1 1045 -
118447 479 J.K.Andersen 2007-10-24 14k 1 14473 -
120457 619 J.K.Andersen 2007-10-24 1.2k 1 1261 -
120997 343 J.K.Andersen 2007-10-24 2.1k 1 2121 -
121061 479 J.K.Andersen 2007-10-24 2.3k 2 2338 -
122017 582 J.K.Andersen 2007-10-24 1.2k 1 1257 -
135787 369 J.K.Andersen 2007-10-24 7.7k 1 7721 -
170467 411 J.K.Andersen 2007-10-24 55k 1 55273 -
173467 408 J.K.Andersen 2007-10-24 6.9k 1 6925 -
173587 235 J.K.Andersen 2007-10-24 172k 1 172609 -
175567 411 K.Bonath 2010-03-28 1040k 1 - -
179677 625 J.K.Andersen 2007-10-24 2.7k 1 2729 -
185347 526 J.K.Andersen 2007-10-24 1.1k 1 1189 -
190357 203 J.K.Andersen 2007-10-24 15k 1 15465 -
190927 518 J.K.Andersen 2007-10-24 72k 1 72289 -
207397 525 J.K.Andersen 2007-10-24 5.6k 1 5609 -
209737 406 J.K.Andersen 2007-10-24 1.3k 1 1313 -
230407 291 J.K.Andersen 2007-10-24 1.1k 1 1105 -
230827 495 J.K.Andersen 2007-10-24 4.1k 1 4177 -
233221 618 J.K.Andersen 2007-10-24 1k 1 1021 -
239107 153 K.Bonath 2010-03-28 1040k 1 - -
246787 219 J.K.Andersen 2007-10-24 1k 1 1081 -