The even Riesel-Problem

Started: Nov 24, 2007
Last update: Dec 06, 2007

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 :

(yellow: reserved)

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

k nash
weight		 contributor last edit search
limit n		 small n
prime(s)		 next
prime n		 remaining prime n
37 630 RPS et al. - 585k 1 2553 4893, 7897, 14353, 32125, 51477, 78973, 341365
337 286 PrimeSearch 2001-2003 600k 1 11677 12101, 44149, 72997, 147929, 171509
1589 396 kar_bon 03.12.2007 100k 4 1620 15480, 28444
1721 313 kar_bon 03.12.2007 100k 2 1034 9818, 75818
1807 296 kar_bon 03.12.2007 100k 1 1369 -
2257 501 gd_barnes
kar_bon
Thomas		 05.07.2007
05.12.2007
2007		 10k
10k-200k
200k-350k		 1, 5 1297 5345, 11393, 20333, 44513, 66893
2317 460 gd_barnes
Thomas		 05.07.2007
2007		 10k
200k-350k		 5 2805 4345
2683 230 amphoria 02.07.2007 1.2M 7 2239 -
3775 727 gd_barnes 05.07.2007 10k 1 1297 -
5857 541 gd_barnes 05.07.2007 10k 5 4973 5909
6869 350 Andersen 24.10.2007 45k 4 45084 -
10021 513 kar_bon 06.12.2007 97k 3 138k 27083, 77673, 78611, 90561
11887 614 Andersen 24.10.2007 1,1k 1, 5 1189 -
12401 306 Andersen 24.10.2007 26k 2 26522 -
17861 271 jasong
kar_bon		 13.10.2007
26.11.2007		 294k 2 98954 256010
18089 386 Andersen 24.10.2007 1,1k 4 1124 -
23651 338 jasong 13.10.2007 237k 2 237506 -
24161 230 Andersen 24.10.2007 8.5k 2 8570 -
31453 242 Andersen 24.10.2007 1.3k 3 1371 -
31841 332 Andersen 24.10.2007 1k 2 1010 -
32257 367 Andersen 24.10.2007 1.9k 1 1985 -
33373 226 Andersen 24.10.2007 5.2k 3 5283 -
39817 235 Andersen 24.10.2007 1.8k 1 1801 -
43151 556 Andersen 24.10.2007 23.2k 2 23286 -
46411 777 Andersen 24.10.2007 2k 1 2027 -
47653 467 Andersen 24.10.2007 1k 3 1083 -
55687 429 Andersen 24.10.2007 1.5k 1 1597 -
58331 501 Andersen 24.10.2007 1.5k 2 1506 -
63367 542 Andersen 24.10.2007 1k 1 1129 -
67001 291 Andersen 24.10.2007 9.5k 2 9506 -
74857 747 Andersen 24.10.2007 1k 1 1121 -
77167 349 jasong 13.10.2007 153k 1 153441 -
79601 766 Andersen 24.10.2007 3.5k 2 3542 -
80771 396 Andersen 24.10.2007 9.4k 2 9482 -
88115 957 Andersen 24.10.2007 2.4k 2 2468 -
90907 317 Andersen 24.10.2007 4.6k 1 4689 -
112391 478 Andersen 24.10.2007 159k 2 159730 -
114367 423 Andersen 24.10.2007 1.6k 1 1681 -
115451 409 Andersen 24.10.2007 6.2k 2 6218 -
116257 376 Andersen 24.10.2007 1k 1 1045 -
118447 479 Andersen 24.10.2007 14k 1 14473 -
120457 619 Andersen 24.10.2007 1.2k 1 1261 -
120997 343 Andersen 24.10.2007 2.1k 1 2121 -
121061 479 Andersen 24.10.2007 2.3k 2 2338 -
122017 582 Andersen 24.10.2007 1.2k 1 1257 -
135787 369 Andersen 24.10.2007 7.7k 1 7721 -
170467 411 Andersen 24.10.2007 55k 1 55273 -
173467 408 Andersen 24.10.2007 6.9k 1 6925 -
173587 235 Andersen 24.10.2007 172k 1 172609 -
175567 411 jasong
kar_bon		 29.10.2007
28.11.2007		 525k
570k		 1 - -
179677 625 Andersen 24.10.2007 2.7k 1 2729 -
185347 526 Andersen 24.10.2007 1.1k 1 1189 -
190357 203 Andersen 24.10.2007 15k 1 15465 -
190927 518 Andersen 24.10.2007 72k 1 72289 -
207397 525 Andersen 24.10.2007 5.6k 1 5609 -
209737 406 Andersen 24.10.2007 1.3k 1 1313 -
230407 291 Andersen 24.10.2007 1.1k 1 1105 -
230827 495 Andersen 24.10.2007 4.1k 1 4177 -
233221 618 Andersen 24.10.2007 1k 1 1021 -
239107 153 jasong
kar_bon		 29.10.2007
28.11.2007		 564k
789k		 1 - -
246787 219 Andersen 24.10.2007 1k 1 1081 -