Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Even Riesel Problem"
(The data table is missing (cue to kar_bon, who I know patrols recent changes).) |
m (correct name) |
||
(3 intermediate revisions by 2 users not shown) | |||
Line 1: | Line 1: | ||
{{DISPLAYTITLE:The Even Riesel Problem}} | {{DISPLAYTITLE:The Even Riesel Problem}} | ||
==Overview== | ==Overview== | ||
− | The [[Riesel problem]] | + | The [[Riesel problem 1|Riesel problem]] is to find the smallest [[Riesel number]] {{Vk}} (odd) such that {{Kbn|k|2|n}} is composite for every {{Vn}} ≥ 1.<br> |
− | + | This page was inspired by two threads of the [[MersenneForum]] [http://www.mersenneforum.org/showthread.php?t=9444 here] and [http://www.mersenneforum.org/showthread.php?t=9440 here] started by (jasong).<br> | |
− | This page was inspired by two threads of the [[MersenneForum]] [http://www.mersenneforum.org/showthread.php?t=9444 here] and [http://www.mersenneforum.org/showthread.php?t=9440 here] started by (jasong). | + | Except a few numbers of the odd {{Vk}}'s of the Riesel problem a prime was found (mostly a higher {{Vn}}). But what about {{Vk}}'s with only a prime with very low {{Vn}}, say {{Vn}} = 1?<br> |
− | + | For example: [[Riesel_prime_2_17861|{{Vk}} = 17861]] is prime for {{Vn}} = 2 and no other {{Vn}} < 50000. So the even value {{Vk}} = 17861 • 2 • 2 = 71444 has no prime for {{Vn}} < 49998.<br> | |
− | Except a few numbers of the odd {{Vk}}'s of the Riesel problem a prime was found (mostly a higher {{Vn}}). But what about {{Vk}}'s with only a prime with very low {{Vn}}, say {{Vn}} = 1? | + | Accordingly there comes up a question: Is there any even {{Vk}} for which {{Kbn|k|2|n}} is never prime? |
− | |||
− | For example: [[Riesel_prime_2_17861|{{Vk}} = 17861]] is prime for {{Vn}} = 2 and no other {{Vn}} < 50000. So the even value {{Vk}} = 17861 • 2 • 2 = 71444 has no prime for {{Vn}} < 49998. | ||
− | |||
− | Accordingly there comes up a question: Is there any even {{Vk}} for which {{ | ||
==Data== | ==Data== | ||
− | The table contains all 61 odd {{Vk}} < 254601 which got only small prime(s) for {{Vn}} < 10 and no other for {{Vn}} < 1000. | + | The table contains all 61 odd {{Vk}} < 254601 which got only small prime(s) for {{Vn}} < 10 and no other for {{Vn}} < 1000.<br> |
− | 9 candidates of them got no other prime for {{Vn}} < 50000. | + | 9 candidates of them got no other prime for {{Vn}} < 50000.<br> |
− | These computations were made by [[Jens | + | These computations were made by [[Jens Kruse Andersen]] and (jasong) in Oct 2007. |
− | ( | + | {| class="wikitable" |
+ | ! {{Vk}} !! [[Nash weight]] !! Contributor !! Last edit !! small {{Vn}} !! next prime | ||
+ | |- | ||
+ | | [[Riesel prime 2 37|37]] || 630 || [[Riesel Prime Search]] || - || 1 || 2553 | ||
+ | |- | ||
+ | | [[Riesel prime 2 337|337]] || 286 || [[NPLB]] || 2008-09-15 || 1 || 11677 | ||
+ | |- | ||
+ | | [[Riesel prime 2 1589|1589]] || 396 || [[Karsten Bonath]] || 2007-12-03 || 4 || 1620 | ||
+ | |- | ||
+ | | [[Riesel prime 2 1721|1721]] || 313 || [[Karsten Bonath]] || 2007-12-03 || 2 || 1034 | ||
+ | |- | ||
+ | | [[Riesel prime 2 1807|1807]] || 296 || [[Karsten Bonath]] || 2007-12-03 || 1 || 1369 | ||
+ | |- | ||
+ | | [[Riesel prime 2 2257|2257]] || 501 || [[Karsten Bonath]] || 2007-12-05 || 1, 5 || 1297 | ||
+ | |- | ||
+ | | [[Riesel prime 2 2317|2317]] || 460 || [[Karsten Bonath]] || 2007-12-22 || 5 || 2805 | ||
+ | |- | ||
+ | | [[Riesel prime 2 2683|2683]] || 230 || [[David Metcalfe]] || 2007-07-02 || 7 || 2239 | ||
+ | |- | ||
+ | | [[Riesel prime 2 3775|3775]] || 727 || [[Gary Barnes]] || 2007-07-05 || 1 || 1297 | ||
+ | |- | ||
+ | | [[Riesel prime 2 5857|5857]] || 541 || [[Gary Barnes]] || 2007-07-05 || 5 || 4973 | ||
+ | |- | ||
+ | | [[Riesel prime 2 6869|6869]] || 350 || [[Jens Kruse Andersen]] || 2007-10-24 || 4 || 45084 | ||
+ | |- | ||
+ | | [[Riesel prime 2 10021|10021]] || 513 || [[Karsten Bonath]] || 2011-10-04 || 3 || 1835 | ||
+ | |- | ||
+ | | [[Riesel prime 2 11887|11887]] || 614 || [[Karsten Bonath]] || 2007-10-24 || 1, 5 || 1189 | ||
+ | |- | ||
+ | | [[Riesel prime 2 12401|12401]] || 306 || [[Karsten Bonath]] || 2010-07-20 || 2 || 26522 | ||
+ | |- | ||
+ | | [[Riesel prime 2 17861|17861]] || 271 || [[Karsten Bonath]] || 2007-11-26 || 2 || 98954 | ||
+ | |- | ||
+ | | [[Riesel prime 2 18089|18089]] || 386 || [[Jens Kruse Andersen]] || 2007-10-24 || 4 || 1124 | ||
+ | |- | ||
+ | | [[Riesel prime 2 23651|23651]] || 338 || (jasong) || 2007-10-13 || 2 || 237506 | ||
+ | |- | ||
+ | | [[Riesel prime 2 24161|24161]] || 230 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 8570 | ||
+ | |- | ||
+ | | [[Riesel prime 2 31453|31453]] || 242 || [[Jens Kruse Andersen]] || 2007-10-24 || 3 || 1371 | ||
+ | |- | ||
+ | | [[Riesel prime 2 31841|31841]] || 332 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 1010 | ||
+ | |- | ||
+ | | [[Riesel prime 2 32257|32257]] || 367 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1985 | ||
+ | |- | ||
+ | | [[Riesel prime 2 33373|33373]] || 226 || [[Jens Kruse Andersen]] || 2007-10-24 || 3 || 5283 | ||
+ | |- | ||
+ | | [[Riesel prime 2 39817|39817]] || 235 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1801 | ||
+ | |- | ||
+ | | [[Riesel prime 2 43151|43151]] || 556 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 23286 | ||
+ | |- | ||
+ | | [[Riesel prime 2 46411|46411]] || 777 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 2027 | ||
+ | |- | ||
+ | | [[Riesel prime 2 47653|47653]] || 467 || [[Jens Kruse Andersen]] || 2007-10-24 || 3 || 1083 | ||
+ | |- | ||
+ | | [[Riesel prime 2 55687|55687]] || 429 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1597 | ||
+ | |- | ||
+ | | [[Riesel prime 2 58331|58331]] || 501 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 1506 | ||
+ | |- | ||
+ | | [[Riesel prime 2 63367|63367]] || 542 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1129 | ||
+ | |- | ||
+ | | [[Riesel prime 2 67001|67001]] || 291 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 9506 | ||
+ | |- | ||
+ | | [[Riesel prime 2 74857|74857]] || 747 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1121 | ||
+ | |- | ||
+ | | [[Riesel prime 2 77167|77167]] || 349 || (jasong) || 2007-10-13 || 1 || 153441 | ||
+ | |- | ||
+ | | [[Riesel prime 2 79601|79601]] || 766 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 3542 | ||
+ | |- | ||
+ | | [[Riesel prime 2 80771|80771]] || 396 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 9482 | ||
+ | |- | ||
+ | | [[Riesel prime 2 88115|88115]] || 957 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 2468 | ||
+ | |- | ||
+ | | [[Riesel prime 2 90907|90907]] || 317 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 4689 | ||
+ | |- | ||
+ | | [[Riesel prime 2 112391|112391]] || 478 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 159730 | ||
+ | |- | ||
+ | | [[Riesel prime 2 114367|114367]] || 423 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1681 | ||
+ | |- | ||
+ | | [[Riesel prime 2 115451|115451]] || 409 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 6218 | ||
+ | |- | ||
+ | | [[Riesel prime 2 116257|116257]] || 376 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1045 | ||
+ | |- | ||
+ | | [[Riesel prime 2 118447|118447]] || 479 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 14473 | ||
+ | |- | ||
+ | | [[Riesel prime 2 120457|120457]] || 619 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1261 | ||
+ | |- | ||
+ | | [[Riesel prime 2 120997|120997]] || 343 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 2121 | ||
+ | |- | ||
+ | | [[Riesel prime 2 121061|121061]] || 479 || [[Jens Kruse Andersen]] || 2007-10-24 || 2 || 2338 | ||
+ | |- | ||
+ | | [[Riesel prime 2 122017|122017]] || 582 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1257 | ||
+ | |- | ||
+ | | [[Riesel prime 2 135787|135787]] || 369 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 7721 | ||
+ | |- | ||
+ | | [[Riesel prime 2 170467|170467]] || 411 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 55273 | ||
+ | |- | ||
+ | | [[Riesel prime 2 173467|173467]] || 408 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 6925 | ||
+ | |- | ||
+ | | [[Riesel prime 2 173587|173587]] || 235 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 172609 | ||
+ | |- | ||
+ | | class="color-Reserved" | [[Riesel prime 2 175567|175567]] || 411 || [[CRUS Even Riesel]] || {{Multi Reservation:15-Date}} || 1 || >{{Num|{{Multi Reservation:15-NMax}}}} | ||
+ | |- | ||
+ | | [[Riesel prime 2 179677|179677]] || 625 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 2729 | ||
+ | |- | ||
+ | | [[Riesel prime 2 185347|185347]] || 526 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1189 | ||
+ | |- | ||
+ | | [[Riesel prime 2 190357|190357]] || 203 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 15465 | ||
+ | |- | ||
+ | | [[Riesel prime 2 190927|190927]] || 518 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 72289 | ||
+ | |- | ||
+ | | [[Riesel prime 2 207397|207397]] || 525 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 5609 | ||
+ | |- | ||
+ | | [[Riesel prime 2 209737|209737]] || 406 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1313 | ||
+ | |- | ||
+ | | [[Riesel prime 2 230407|230407]] || 291 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1105 | ||
+ | |- | ||
+ | | [[Riesel prime 2 230827|230827]] || 495 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 4177 | ||
+ | |- | ||
+ | | [[Riesel prime 2 233221|233221]] || 618 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1021 | ||
+ | |- | ||
+ | | class="color-Reserved" | [[Riesel prime 2 239107|239107]] || 153 || [[CRUS Even Riesel]] || {{Multi Reservation:15-Date}} || 1 || >{{Num|{{Multi Reservation:15-NMax}}}} | ||
+ | |- | ||
+ | | [[Riesel prime 2 246787|246787]] || 219 || [[Jens Kruse Andersen]] || 2007-10-24 || 1 || 1081 | ||
+ | |} | ||
==Status== | ==Status== | ||
− | Only | + | Only two of these 61 candidates got no higher prime {{Vn}}: [[Riesel_prime_2_175567|{{Vk}} = 175567]] and [[Riesel_prime_2_239107|{{Vk}} = 239107]] (see the [[CRUS Even Riesel]] project). |
{{Navbox Riesel primes}} | {{Navbox Riesel primes}} | ||
− | [[Category: | + | [[Category:Riesel prime conjectures]] |
Latest revision as of 08:20, 28 May 2024
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 Kruse 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 : |
Miscellaneous |
Tables |
Categories |
Others |
Other categories |
Other bases |