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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).
| Base = 2 : |
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