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paulunderwood 2017-10-27 15:24

[QUOTE=GP2;470443]The 318th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7080247[/M].

This is a new record for Mersenne PRPs, the previous record was [M]M5240707[/M].[/QUOTE]

[CODE]time ../../coding/gwnum/lucasPRP M7080247-cofactor 1 2 7080247 -1
Lucas testing on x^2 - 3*x + 1 ...
Is Lucas PRP!

real 135m13.604s
user 499m40.712s
sys 12m34.268s[/CODE]

Congrats!

kruoli 2017-10-28 20:39

[QUOTE=GP2;470443]The 318th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7080247[/M].[/QUOTE]

Are you sure? :D You said, M20521 is the 318th, too!

James Heinrich 2017-10-28 20:48

I [url=http://www.mersenne.ca/prp.php]count 319[/url].

GP2 2017-10-30 19:35

Here's an attempt to reconstruct the timeline of recent PRP discoveries.

There are two sources of PRP discoveries: large exponents which were previously untested, and small exponents for which a new factor was very recently found.

For small exponents, the date of discovery of the last factor is the earliest of the dates in Primenet and FactorDB. In such cases the PRP test happened very soon after, either at Mersenne.ca or automatically at FactorDB. It may not be meaningful to talk about the discoverer in such cases, because the PRP test for such small exponents is practically instantaneous, and FactorDB usually carries it out automatically for very small Mersenne exponents as soon as the factor is submitted.

For exponents above sequence number 317, Primenet shows accurate discover and date of discovery.
For the ones below this sequence number, the Primenet data reflects the date of retest/double checks, since PRP testing was added to Primenet only in September 2017.

Note that [M]M157457[/M] does not appear in the list below. It appears in the Lifchitz & Lifchitz PRP Top listing with date 2016-07, but I think this is inaccurate. It was discovered earlier, I'm not sure when, but for some reason was not added to their listing until this later date. Maybe someone has further information?

[CODE]
Seq Exponent last factor PRP tested Source
=== ======== ========== ========== =======
274 [M]432457[/M] 2010-02-18 2013-09≈ [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282^x-1%29%2F%3F&action=Search"]Lifchitz[/URL] Never Odd or Even
275 [M]696343[/M] 2014-01-14 2014-02≈ [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282^x-1%29%2F%3F&action=Search"]Lifchitz[/URL] Never Odd or Even
276 [M]1010623[/M] old 2014-02≈ [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282^x-1%29%2F%3F&action=Search"]Lifchitz[/URL] Never Odd or Even
277 [M]1304983[/M] old 2014-03≈ [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282^x-1%29%2F%3F&action=Search"]Lifchitz[/URL] Never Odd or Even
278 [M]1129[/M] 2014-05-23≈
279 [M]1151[/M] 2014-05-23≈
280 [M]1153[/M] 2014-05-23≈
281 [M]576551[/M] 2014-03-18 2014-06-13 [URL="http://mersenneforum.org/showthread.php?t=19407&p=375749"]MersForum[/URL] alpertron
282 [M]1193[/M] 2014-08-22≈
283 [M]2327417[/M] old 2014-08-30 [URL="http://mersenneforum.org/showthread.php?t=19407&p=381734"]MersForum[/URL] axn
284 [M]270059[/M] 2014-09-05 2014-09-05 [URL="http://mersenneforum.org/showthread.php?t=19407&p=382224"]MersForum[/URL] alpertron
285 [M]19121[/M] 2014-09-19 2014-09-20 [URL="http://mersenneforum.org/showthread.php?t=19407&p=383494"]MersForum[/URL] alpertron
286 [M]1093[/M] 2014-09-15≈ 2014-09-20 [URL="http://mersenneforum.org/showthread.php?t=19407&p=383518"]MersForum[/URL] houding?
287 [M]1109[/M] 2014-09-21≈
288 [M]750151[/M] 2014-10-05 2014-10-05 [URL="http://mersenneforum.org/showthread.php?t=19407&p=384419"]MersForum[/URL] alpertron
289 [M]1117[/M] 2014-11-25≈
290 [M]3464473[/M] old 2014-10-12 [URL="http://mersenneforum.org/showthread.php?t=19407&p=385016"]MersForum[/URL] axn
291 [M]488441[/M] 2014-12-11 2014-12-11 [URL="http://mersenneforum.org/showthread.php?t=19407&p=389763"]MersForum[/URL] alpertron
292 [M]1123[/M] 2014-12-23≈
293 [M]440399[/M] 2015-01-02 2015-01-02 [URL="http://mersenneforum.org/showthread.php?t=19407&p=391480"]MersForum[/URL] alpertron
294 [M]1171[/M] 2015-01-11≈
295 [M]10433[/M] 2015-04-14 2015-04-14 [URL="http://mersenneforum.org/showthread.php?t=19407&p=400046"]MersForum[/URL] Batalov
296 [M]35339[/M] 2015-04-01 2015-04-21 [URL="http://mersenneforum.org/showthread.php?t=19407&p=400573"]MersForum[/URL] Batalov
297 [M]41681[/M] 2015-04-26 2015-04-26 [URL="http://mersenneforum.org/showthread.php?t=19407&p=400944"]MersForum[/URL] Batalov
298 [M]991[/M] 2015-06-17≈
299 [M]1790743[/M] 2015-06-25 2015-06-25 [URL="http://mersenneforum.org/showthread.php?t=19407&p=404786"]MersForum[/URL] alpertron
300 [M]675977[/M] 2015-07-09 2015-07-09 [URL="http://mersenneforum.org/showthread.php?t=19407&p=405564"]MersForum[/URL] alpertron
301 [M]1409[/M] 2016-02-29≈
302 [M]4187251[/M] old 2016-05-30 [URL="http://mersenneforum.org/showthread.php?t=19157&p=435144"]MersForum[/URL] Never Odd or Even
303 [M]5240707[/M] old 2016-07-30 [URL="http://mersenneforum.org/showthread.php?t=19157&p=439079"]MersForum[/URL] Never Odd or Even
304 [M]822971[/M] 2016-09-09 2016-09-14 [URL="http://mersenneforum.org/showthread.php?t=19157&p=442582"]MersForum[/URL] Robert Kinser
305 [M]5233[/M] 2016-09-28 2016-09-28 [URL="http://mersenneforum.org/showthread.php?t=13977&p=443736"]MersForum[/URL] GP2
306 [M]151013[/M] 2016-10-28 2016-11-14 [URL="http://mersenneforum.org/showthread.php?t=19407&p=447216"]MersForum[/URL] Robert Kinser
307 [M]25243[/M] 2016-12-05 2016-12-05 [URL="http://mersenneforum.org/showthread.php?t=19407&p=448486"]MersForum[/URL] GP2
308 [M]25933[/M] 2016-12-11 2016-12-11 [URL="http://mersenneforum.org/showthread.php?t=19407&p=448932"]MersForum[/URL] GP2
309 [M]4834891[/M] 2008-09-30 2016-12-12 [URL="http://mersenneforum.org/showthread.php?t=19407&p=449044"]MersForum[/URL] GP2
310 [M]53381[/M] 2016-12-18 2016-12-21 [URL="http://mersenneforum.org/showthread.php?t=19407&p=449724"]MersForum[/URL]
311 [M]84211[/M] 2017-02-28 2017-03-03 [URL="http://mersenneforum.org/showthread.php?t=19407&p=454160"]MersForum[/URL]
312 [M]175631[/M] 2017-03-03 2017-03-09 [URL="http://mersenneforum.org/showthread.php?t=19407&p=454563"]MersForum[/URL] Robert Kinser
313 [M]12569[/M] 2017-04-05 2017-04-05 [URL="http://mersenneforum.org/showthread.php?t=19407&p=456219"]MersForum[/URL] GP2
314 [M]174533[/M] 2017-05-29 2017-06-02 [URL="http://mersenneforum.org/showthread.php?t=19407&p=460355"]MersForum[/URL] alpertron
315 [M]611999[/M] 2017-06-08 2017-06-09 [URL="http://mersenneforum.org/showthread.php?t=19407&p=460879"]MersForum[/URL] alpertron
316 [M]1471[/M] 2017-08-31≈ [URL="http://mersenneforum.org/showthread.php?t=19407&p=466979"]MersForum[/URL]
317 [M]8243[/M] 2017-10-10 2017-10-10 Primenet YarBer
318 [M]20521[/M] 2017-10-18 2017-10-18 Primenet Oliver Kruse
319 [M]7080247[/M] 2016-12-06 2017-10-27 Primenet GP2
[/CODE]

Let me know of any inaccuracies.

Did Mersenne.ca keep track of the exact dates that PRPs were reported?

James Heinrich 2017-10-30 19:44

[QUOTE=GP2;470635]Did Mersenne.ca keep track of the exact dates that PRPs were reported?[/QUOTE]There is a last-modified column in the table, but I wouldn't necessarily count on it as being accurate, data may have been massaged or reformated reinserted or otherwise modified at some time after the initial discovery. These are the dates I have, but I don't expect that they're too helpful:[code]mysql> SELECT `rankorder`, `exponent`, `last_modified` FROM `prp` WHERE (`rankorder` > 0) AND (`cofactors` <> "") ORDER BY `rankorder` ASC;
+------+----------+---------------------+
| rank | exponent | last_modified |
+------+----------+---------------------+
| 1 | 11 | 2017-02-11 14:10:46 |
| 2 | 23 | 2017-02-11 14:17:34 |
| 3 | 29 | 2017-02-11 14:17:34 |
| 4 | 37 | 2017-02-11 14:17:34 |
| 5 | 41 | 2017-02-11 14:17:34 |
| 6 | 43 | 2017-02-11 14:17:34 |
| 7 | 47 | 2017-02-11 14:17:34 |
| 8 | 53 | 2017-02-13 07:34:59 |
| 9 | 59 | 2016-06-25 12:08:26 |
| 10 | 67 | 2017-02-11 14:17:34 |
| 11 | 71 | 2017-02-11 14:17:34 |
| 12 | 73 | 2017-02-11 14:17:34 |
| 13 | 79 | 2017-02-11 14:17:34 |
| 14 | 83 | 2017-02-11 14:17:34 |
| 15 | 97 | 2017-02-11 14:17:34 |
| 16 | 101 | 2016-06-24 23:16:46 |
| 17 | 103 | 2016-06-24 23:16:46 |
| 18 | 109 | 2016-06-24 23:16:46 |
| 19 | 113 | 2016-06-24 23:16:46 |
| 20 | 131 | 2016-06-24 23:16:46 |
| 21 | 137 | 2016-06-24 23:16:46 |
| 22 | 139 | 2016-06-24 23:16:46 |
| 23 | 149 | 2016-06-24 23:16:46 |
| 24 | 151 | 2016-06-24 23:16:46 |
| 25 | 157 | 2016-06-24 23:16:46 |
| 26 | 163 | 2016-06-24 23:16:46 |
| 27 | 167 | 2016-06-24 23:16:46 |
| 28 | 173 | 2016-06-24 23:16:46 |
| 29 | 179 | 2016-06-24 23:16:46 |
| 30 | 181 | 2016-06-24 23:16:46 |
| 31 | 191 | 2017-02-11 14:23:40 |
| 32 | 193 | 2016-06-24 23:16:46 |
| 33 | 197 | 2016-06-24 23:16:46 |
| 34 | 199 | 2016-06-24 23:16:46 |
| 35 | 211 | 2016-06-24 23:16:46 |
| 36 | 223 | 2017-02-11 14:23:40 |
| 37 | 227 | 2016-06-24 23:16:46 |
| 38 | 229 | 2016-06-24 23:16:46 |
| 39 | 233 | 2016-06-24 23:16:46 |
| 40 | 239 | 2016-06-25 12:08:49 |
| 41 | 241 | 2016-06-24 23:16:46 |
| 42 | 251 | 2017-02-11 14:23:40 |
| 43 | 257 | 2016-06-24 23:16:46 |
| 44 | 263 | 2016-06-24 23:16:46 |
| 45 | 269 | 2016-06-24 23:16:46 |
| 46 | 271 | 2016-06-24 23:16:46 |
| 47 | 277 | 2016-06-24 23:16:46 |
| 48 | 281 | 2017-02-11 14:23:40 |
| 49 | 283 | 2016-06-24 23:16:46 |
| 50 | 293 | 2016-06-24 23:16:46 |
| 51 | 307 | 2016-06-24 23:16:46 |
| 52 | 311 | 2016-06-24 23:16:46 |
| 53 | 313 | 2016-06-24 23:16:46 |
| 54 | 317 | 2016-06-24 23:16:46 |
| 55 | 331 | 2016-06-24 23:16:46 |
| 56 | 337 | 2016-06-24 23:16:46 |
| 57 | 347 | 2016-06-24 23:16:46 |
| 58 | 349 | 2016-06-24 23:16:46 |
| 59 | 353 | 2016-06-24 23:16:46 |
| 60 | 359 | 2017-02-11 14:23:40 |
| 61 | 367 | 2016-06-24 23:16:46 |
| 62 | 373 | 2017-02-11 14:23:40 |
| 63 | 379 | 2016-06-24 23:16:46 |
| 64 | 383 | 2017-02-11 14:23:40 |
| 65 | 389 | 2016-06-24 23:16:46 |
| 66 | 397 | 2017-02-11 14:23:40 |
| 67 | 401 | 2016-06-24 23:16:46 |
| 68 | 409 | 2016-06-24 23:16:46 |
| 69 | 419 | 2016-06-24 23:16:46 |
| 70 | 421 | 2016-06-24 23:16:46 |
| 71 | 431 | 2017-02-11 14:23:40 |
| 72 | 433 | 2016-06-24 23:16:46 |
| 73 | 439 | 2016-06-24 23:16:46 |
| 74 | 443 | 2016-06-24 23:16:46 |
| 75 | 449 | 2016-06-24 23:16:46 |
| 76 | 457 | 2016-06-24 23:16:46 |
| 77 | 461 | 2016-06-24 23:16:46 |
| 78 | 463 | 2016-06-24 23:16:46 |
| 79 | 467 | 2016-06-24 23:16:46 |
| 80 | 479 | 2016-06-24 23:16:46 |
| 81 | 487 | 2016-06-24 23:16:46 |
| 82 | 491 | 2017-02-11 14:23:40 |
| 83 | 499 | 2016-06-24 23:16:46 |
| 84 | 503 | 2016-06-24 23:16:46 |
| 85 | 509 | 2016-06-24 23:16:46 |
| 86 | 523 | 2016-06-24 23:16:46 |
| 87 | 541 | 2016-06-24 23:16:46 |
| 88 | 547 | 2016-06-24 23:16:46 |
| 89 | 557 | 2016-06-24 23:16:46 |
| 90 | 563 | 2016-06-24 23:16:46 |
| 91 | 569 | 2016-06-24 23:16:46 |
| 92 | 571 | 2016-06-24 23:16:46 |
| 93 | 577 | 2016-06-24 23:16:46 |
| 94 | 587 | 2016-06-24 23:16:46 |
| 95 | 593 | 2016-06-24 23:16:46 |
| 96 | 599 | 2016-06-24 23:16:46 |
| 97 | 601 | 2016-06-24 23:16:46 |
| 98 | 613 | 2016-06-24 23:16:46 |
| 99 | 617 | 2016-06-24 23:16:46 |
| 100 | 619 | 2016-06-24 23:16:46 |
| 101 | 631 | 2016-06-24 23:16:46 |
| 102 | 641 | 2016-06-24 23:16:46 |
| 103 | 643 | 2016-06-24 23:16:46 |
| 104 | 647 | 2016-06-24 23:16:46 |
| 105 | 653 | 2016-06-24 23:16:46 |
| 106 | 659 | 2016-06-24 23:16:46 |
| 107 | 661 | 2016-06-24 23:16:46 |
| 108 | 673 | 2016-06-24 23:16:46 |
| 109 | 677 | 2016-06-24 23:16:46 |
| 110 | 683 | 2016-06-24 23:16:46 |
| 111 | 691 | 2016-06-24 23:16:46 |
| 112 | 701 | 2016-06-24 23:16:46 |
| 113 | 709 | 2016-06-24 23:16:46 |
| 114 | 719 | 2016-06-24 23:16:46 |
| 115 | 727 | 2016-06-24 23:16:46 |
| 116 | 733 | 2016-06-24 23:16:46 |
| 117 | 739 | 2016-06-24 23:16:46 |
| 118 | 743 | 2016-06-24 23:16:46 |
| 119 | 751 | 2016-06-24 23:16:46 |
| 120 | 757 | 2016-06-24 23:16:46 |
| 121 | 761 | 2016-06-24 23:16:46 |
| 122 | 769 | 2016-06-24 23:16:46 |
| 123 | 773 | 2016-06-24 23:16:46 |
| 124 | 787 | 2016-06-24 23:16:46 |
| 125 | 797 | 2016-06-24 23:16:46 |
| 126 | 809 | 2017-02-11 14:23:41 |
| 127 | 811 | 2016-06-24 23:16:46 |
| 128 | 821 | 2016-06-24 23:16:46 |
| 129 | 823 | 2016-06-24 23:16:46 |
| 130 | 827 | 2016-06-24 23:16:46 |
| 131 | 829 | 2016-06-24 23:16:46 |
| 132 | 839 | 2016-06-24 23:16:46 |
| 133 | 853 | 2016-06-24 23:16:46 |
| 134 | 857 | 2016-06-24 23:16:46 |
| 135 | 859 | 2016-06-24 23:16:46 |
| 136 | 863 | 2016-06-24 23:16:46 |
| 137 | 877 | 2016-06-24 23:16:46 |
| 138 | 881 | 2016-06-24 23:16:46 |
| 139 | 883 | 2016-06-24 23:16:46 |
| 140 | 887 | 2016-06-24 23:16:46 |
| 141 | 907 | 2016-06-24 23:16:46 |
| 142 | 911 | 2016-06-24 23:16:46 |
| 143 | 919 | 2016-06-24 23:16:46 |
| 144 | 929 | 2016-06-24 23:16:46 |
| 145 | 937 | 2016-06-24 23:16:46 |
| 146 | 941 | 2016-06-24 23:16:46 |
| 147 | 947 | 2016-06-24 23:16:46 |
| 148 | 953 | 2016-06-24 23:16:46 |
| 149 | 967 | 2016-06-24 23:16:46 |
| 150 | 971 | 2016-06-24 23:16:46 |
| 151 | 977 | 2016-06-24 23:16:46 |
| 152 | 983 | 2016-06-24 23:16:46 |
| 153 | 991 | 2016-06-24 23:16:46 |
| 154 | 997 | 2016-06-24 23:16:46 |
| 155 | 1009 | 2016-06-24 23:16:46 |
| 156 | 1013 | 2016-06-24 23:16:46 |
| 157 | 1019 | 2016-06-24 23:16:46 |
| 158 | 1021 | 2016-06-24 23:16:46 |
| 159 | 1031 | 2016-06-24 23:16:46 |
| 160 | 1033 | 2016-06-24 23:16:46 |
| 161 | 1039 | 2016-06-24 23:16:46 |
| 162 | 1049 | 2016-06-24 23:16:46 |
| 163 | 1051 | 2016-06-24 23:16:46 |
| 164 | 1061 | 2016-06-24 23:16:46 |
| 165 | 1063 | 2016-06-24 23:16:46 |
| 166 | 1069 | 2016-06-24 23:16:46 |
| 167 | 1087 | 2016-06-24 23:16:46 |
| 168 | 1091 | 2016-06-24 23:16:46 |
| 169 | 1093 | 2016-06-24 23:16:46 |
| 170 | 1097 | 2016-06-24 23:16:46 |
| 171 | 1103 | 2016-06-24 23:16:46 |
| 172 | 1109 | 2016-06-24 23:16:46 |
| 173 | 1117 | 2016-06-24 23:16:46 |
| 174 | 1123 | 2016-06-24 23:16:46 |
| 175 | 1129 | 2016-06-24 23:16:46 |
| 176 | 1151 | 2016-06-24 23:16:46 |
| 177 | 1153 | 2016-06-24 23:16:46 |
| 178 | 1163 | 2016-06-24 23:16:46 |
| 179 | 1171 | 2016-06-24 23:16:46 |
| 180 | 1181 | 2016-06-24 23:16:46 |
| 181 | 1187 | 2016-06-24 23:16:46 |
| 182 | 1193 | 2016-06-24 23:16:46 |
| 183 | 1201 | 2016-06-24 23:16:46 |
| 184 | 1223 | 2016-06-24 23:16:46 |
| 185 | 1289 | 2016-06-24 23:16:46 |
| 186 | 1301 | 2016-06-24 23:16:46 |
| 187 | 1303 | 2016-06-24 23:16:46 |
| 188 | 1307 | 2016-06-24 23:16:46 |
| 189 | 1321 | 2016-06-24 23:16:46 |
| 190 | 1327 | 2016-06-24 23:16:46 |
| 191 | 1361 | 2016-06-24 23:16:46 |
| 192 | 1373 | 2016-06-24 23:16:46 |
| 193 | 1409 | 2016-06-24 23:16:46 |
| 194 | 1427 | 2016-06-24 23:16:46 |
| 195 | 1459 | 2016-06-24 23:16:46 |
| 196 | 1471 | 2017-09-03 06:58:24 |
| 197 | 1487 | 2016-06-24 23:16:46 |
| 198 | 1531 | 2016-06-24 23:16:46 |
| 199 | 1543 | 2016-06-24 23:16:46 |
| 200 | 1553 | 2016-06-24 23:16:46 |
| 201 | 1559 | 2016-06-24 23:16:46 |
| 202 | 1637 | 2016-06-24 23:16:46 |
| 203 | 1657 | 2016-06-24 23:16:46 |
| 204 | 1693 | 2016-06-24 23:16:46 |
| 205 | 1783 | 2016-06-24 23:16:46 |
| 206 | 1907 | 2016-06-24 23:16:46 |
| 207 | 1997 | 2016-06-24 23:16:46 |
| 208 | 2069 | 2016-06-24 23:16:46 |
| 209 | 2087 | 2016-06-24 23:16:46 |
| 210 | 2243 | 2016-06-24 23:16:46 |
| 211 | 2251 | 2016-06-24 23:16:46 |
| 212 | 2311 | 2016-06-24 23:16:46 |
| 213 | 2381 | 2016-06-24 23:16:46 |
| 214 | 2383 | 2016-06-24 23:16:46 |
| 215 | 2447 | 2016-06-24 23:16:46 |
| 216 | 2549 | 2016-06-24 23:16:46 |
| 217 | 2677 | 2016-06-24 23:16:46 |
| 218 | 2699 | 2016-06-24 23:16:46 |
| 219 | 2837 | 2016-06-24 23:16:46 |
| 220 | 2909 | 2016-06-24 23:16:46 |
| 221 | 2927 | 2016-06-24 23:16:46 |
| 222 | 3041 | 2016-06-24 23:16:46 |
| 223 | 3079 | 2016-06-24 23:16:46 |
| 224 | 3259 | 2016-06-24 23:16:46 |
| 225 | 3359 | 2016-06-24 23:16:46 |
| 226 | 3547 | 2016-06-24 23:16:46 |
| 227 | 3833 | 2016-06-24 23:16:46 |
| 228 | 4127 | 2016-06-24 23:16:46 |
| 229 | 4219 | 2016-06-24 23:16:46 |
| 230 | 4243 | 2016-06-24 23:16:46 |
| 231 | 4729 | 2016-06-24 23:16:46 |
| 232 | 4751 | 2016-06-24 23:16:46 |
| 233 | 4871 | 2016-06-24 23:16:46 |
| 234 | 5087 | 2016-06-24 23:16:46 |
| 235 | 5227 | 2016-06-24 23:16:46 |
| 236 | 5233 | 2016-09-28 17:54:08 |
| 237 | 5689 | 2016-06-24 23:16:46 |
| 238 | 6043 | 2016-06-24 23:16:46 |
| 239 | 6199 | 2016-06-24 23:16:46 |
| 240 | 6337 | 2016-06-24 23:16:46 |
| 241 | 6883 | 2016-06-24 23:16:46 |
| 242 | 7039 | 2016-06-24 23:16:46 |
| 243 | 7331 | 2016-06-24 23:16:46 |
| 244 | 7417 | 2016-06-24 23:16:46 |
| 245 | 7673 | 2016-06-24 23:16:46 |
| 246 | 7757 | 2016-06-24 23:16:46 |
| 247 | 8243 | 2017-10-10 03:54:21 |
| 248 | 8849 | 2016-06-24 23:16:46 |
| 249 | 9697 | 2016-06-24 23:16:46 |
| 250 | 9733 | 2016-06-24 23:16:46 |
| 251 | 9901 | 2016-06-24 23:16:46 |
| 252 | 10007 | 2016-06-24 23:16:46 |
| 253 | 10169 | 2016-06-24 23:16:46 |
| 254 | 10211 | 2016-06-24 23:16:46 |
| 255 | 10433 | 2016-06-24 23:16:46 |
| 256 | 11117 | 2016-06-24 23:16:46 |
| 257 | 11813 | 2016-06-24 23:16:46 |
| 258 | 12451 | 2016-06-24 23:16:46 |
| 259 | 12569 | 2017-04-05 07:37:23 |
| 260 | 14561 | 2016-06-24 23:16:46 |
| 261 | 14621 | 2016-06-24 23:16:46 |
| 262 | 17029 | 2016-06-24 23:16:46 |
| 263 | 17683 | 2016-06-24 23:16:46 |
| 264 | 19121 | 2016-06-24 23:16:46 |
| 265 | 20521 | 2017-10-18 10:13:58 |
| 266 | 20887 | 2016-06-24 23:16:46 |
| 267 | 25243 | 2016-12-05 07:21:16 |
| 268 | 25933 | 2016-12-11 03:53:26 |
| 269 | 26903 | 2016-06-24 23:16:46 |
| 270 | 28759 | 2016-06-24 23:16:46 |
| 271 | 28771 | 2016-06-24 23:16:46 |
| 272 | 29473 | 2016-06-24 23:16:46 |
| 273 | 32531 | 2016-06-24 23:16:46 |
| 274 | 35339 | 2016-06-24 23:16:46 |
| 275 | 41263 | 2016-06-24 23:16:46 |
| 276 | 41521 | 2016-06-24 23:16:46 |
| 277 | 41681 | 2016-06-24 23:16:46 |
| 278 | 53381 | 2016-12-21 19:48:25 |
| 279 | 57131 | 2016-06-24 23:16:46 |
| 280 | 58199 | 2016-06-24 23:16:46 |
| 281 | 63703 | 2016-06-24 23:16:46 |
| 282 | 82939 | 2016-06-24 23:16:46 |
| 283 | 84211 | 2017-03-02 17:17:57 |
| 284 | 86137 | 2016-06-24 23:16:46 |
| 285 | 86371 | 2016-06-24 23:16:46 |
| 286 | 87691 | 2016-06-24 23:16:46 |
| 287 | 106391 | 2016-06-24 23:16:46 |
| 288 | 130439 | 2016-06-24 23:16:46 |
| 289 | 136883 | 2016-06-24 23:16:46 |
| 290 | 151013 | 2016-11-14 01:09:08 |
| 291 | 157457 | 2016-06-24 23:16:46 |
| 292 | 173867 | 2016-06-24 23:16:46 |
| 293 | 174533 | 2017-06-02 14:14:36 |
| 294 | 175631 | 2017-03-08 19:36:24 |
| 295 | 221509 | 2016-06-24 23:16:46 |
| 296 | 270059 | 2016-06-24 23:16:46 |
| 297 | 271211 | 2016-06-24 23:16:46 |
| 298 | 271549 | 2016-06-24 23:16:46 |
| 299 | 406583 | 2016-06-24 23:16:46 |
| 300 | 432457 | 2016-06-24 23:16:46 |
| 301 | 440399 | 2016-06-24 23:16:46 |
| 302 | 488441 | 2016-06-24 23:16:46 |
| 303 | 576551 | 2016-06-24 23:16:46 |
| 304 | 611999 | 2017-06-09 13:14:31 |
| 305 | 675977 | 2016-06-24 23:16:46 |
| 306 | 684127 | 2016-06-24 23:16:46 |
| 307 | 696343 | 2016-06-24 23:16:46 |
| 308 | 750151 | 2016-06-24 23:16:46 |
| 309 | 822971 | 2016-09-12 03:33:27 |
| 310 | 1010623 | 2016-06-24 23:16:46 |
| 311 | 1168183 | 2016-06-24 23:16:46 |
| 312 | 1304983 | 2016-06-24 23:16:46 |
| 313 | 1790743 | 2016-06-24 23:16:46 |
| 314 | 2327417 | 2016-06-24 23:16:46 |
| 315 | 3464473 | 2016-06-24 23:16:46 |
| 316 | 4187251 | 2016-06-24 23:16:46 |
| 317 | 4834891 | 2016-12-12 19:47:52 |
| 318 | 5240707 | 2016-07-30 07:26:52 |
| 319 | 7080247 | 2017-10-27 22:29:31 |
+------+----------+---------------------+
319 rows in set (0.58 sec)[/code]

alpertron 2017-10-31 19:30

[QUOTE=GP2;470635]
Note that [M]M157457[/M] does not appear in the list below. It appears in the Lifchitz & Lifchitz PRP Top listing with date 2016-07, but I think this is inaccurate. It was discovered earlier, I'm not sure when, but for some reason was not added to their listing until this later date. Maybe someone has further information?
[/QUOTE]

From [URL="http://www.mersenneforum.org/showpost.php?p=379457&postcount=171"]post #171[/URL] in this thread you can see that the PRP was discovered before 31 July 2014.

GP2 2017-11-22 06:45

The 320th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M1629469[/M].

It is a semiprime. Its factor was discovered yesterday by VictordeHolland(er) using ECM.

paulunderwood 2017-11-25 00:42

FWIW:

[CODE]time ../../coding/gwnum/lucasPRP M1629469-cofactor 1 2 1629469 -1
Lucas testing on x^2 - 3*x + 1 ...
Is Lucas PRP!

real 8m1.612s
user 25m44.748s
sys 2m31.076s
[/CODE]

Congrats! :smile:

kruoli 2017-11-27 12:17

Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?

Dr Sardonicus 2017-11-27 15:58

[QUOTE=kruoli;472528]Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?[/QUOTE]
Hmm, a PRP-24938. Based on the following, I'd say months to possibly over a year. From the [url=https://en.wikipedia.org/wiki/Elliptic_curve_primality#cite_note-5]Wikipedia page on ECPP[/url],[quote]As of November 2016, the largest prime that has been proved with ECPP method has 34,093 digits.[url=http://primes.utm.edu/top20/page.php?id=27][sup]5[/sup][/url] The certification by Paul Underwood took 14 months using Marcel Martin's Primo software.[/quote]

And, the latest:

[url=http://www.ellipsa.eu/public/primo/top20.html]Ellipsa > Primo Top-20[/url] Certificate for 2[sup]116224[/sup] - 15905 (34987 decimal digits)[quote]The certification of this number was done by Peter Kaiser with Primo 4.1.1 [°]. The certification process took 694 days for the phase 1 and 58 days for the phase 2 using a Dual Intel E3667 processor (16 cores at 3.2 GHz).
[°] The original format-3 certificate (100.9 MB) was updated to a format-4 certificate in order to get a smaller file (75.5 MB). [/quote]

[This was mentioned in this Forum [url=http://www.mersenneforum.org/showpost.php?p=472097&postcount=17]here[/url]]

Also, one of the other Primo top 20, (2[sup]83339[/sup] + 1)/3, which is only slightly larger than the number currently at issue, took 18 months.

Of course, this does not rule out the possibility of a faster primality proof by some other method...

paulunderwood 2017-11-28 20:48

[QUOTE=Dr Sardonicus;472534]

And, the latest:

[url=http://www.ellipsa.eu/public/primo/top20.html]Ellipsa > Primo Top-20[/url] Certificate for 2[sup]116224[/sup] - 15905 (34987 decimal digits)

[/QUOTE]

I have asked Peter to update the Wiki page with his impressive number.

paulunderwood 2017-11-28 20:52

[QUOTE=kruoli;472528]Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?[/QUOTE]

The more cores in one box your throw at it the better. It would top this [URL="http://primes.utm.edu/top20/page.php?id=49"]top20 table[/URL] :smile:

VBCurtis 2017-11-29 02:00

[QUOTE=kruoli;472528]Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?[/QUOTE]

If I wanted to tackle this, where would I reserve it? I don't mind spending 6 months on 6 cores to get it done, but I do mind spending 4 months to discover someone else finished it.

Batalov 2017-11-29 15:34

[QUOTE=VBCurtis;472640]6 months on 6 cores to get it done...[/QUOTE]
This is off by at least an order of magnitude.

paulunderwood 2017-11-29 15:57

(2^83339 + 1)/3 took Tom Wu 374 days on a 6-core 1090T (3.2GHz) if my memory serves me well. There is little or no advantage to using AVX(2) based machines.

Edit: I see Dr. Sardonicus says it took 18 months. I am taking my timings from the d/l cert at ellipsa.eu

Dr Sardonicus 2017-11-29 17:01

[QUOTE=paulunderwood;472664](2^83339 + 1)/3 took Tom Wu 374 days on a 6-core 1090T (3.2GHz) if my memory serves me well. There is little or no advantage to using AVX(2) based machines.

Edit: I see Dr. Sardonicus says it took 18 months. I am taking my timings from the d/l cert at ellipsa.eu[/QUOTE]

I was merely parroting the user comments I found by following the link to the [url=http://primes.utm.edu/primes/page.php?id=118512]Prime database page for (2[sup]83339[/sup] + 1)/3[/url]:

[quote]The certification process took approximately 18 months on a 6-core AMD Phenom II processor.[/quote]

VBCurtis 2017-11-29 18:38

Thanks for the feedback! I'm not keen on a calculation that would take me 9-10 months on my biggest machine; too much risk of someone Amazon-ing it before I finish.

GP2 2017-11-29 19:29

[QUOTE=VBCurtis;472679]Thanks for the feedback! I'm not keen on a calculation that would take me 9-10 months on my biggest machine; too much risk of someone Amazon-ing it before I finish.[/QUOTE]

Two circumstances make that unlikely:

1. The fact that it is a GUI-only program makes it very inconvenient to run on the cloud, especially with spot instances that can terminate/resume at any time. Is it even possible to start/resume the program automatically without manual intervention?

2. In practice, spot market pricing as observed empirically on AWS makes anything larger than 2-core (c4.xlarge) instances not cost-effective, on a cost-per-hour-per-core basis. (On Google Compute Engine, on the other hand, the cost-per-hour-per-core is always the same fixed amount, regardless of the number of cores on a preemptible virtual machine.)

Do Primo benchmarks scale linearly as you increase the number of cores, or is there a penalty for using multicore, similarly to what is seen with mprime?

paulunderwood 2017-11-29 19:45

[QUOTE=GP2;472684]

Do Primo benchmarks scale linearly as you increase the number of cores, or is there a penalty for using multicore, similarly to what is seen with mprime?[/QUOTE]

It is linear -- Primo is [URL="https://en.wikipedia.org/wiki/Embarrassingly_parallel"]embarrassingly parallel[/URL]

Mark Rose 2017-11-29 22:02

[QUOTE=GP2;472684]1. The fact that it is a GUI-only program makes it very inconvenient to run on the cloud, especially with spot instances that can terminate/resume at any time. Is it even possible to start/resume the program automatically without manual intervention?[/QUOTE]

EC2 spot [url=https://aws.amazon.com/blogs/aws/amazon-ec2-update-streamlined-access-to-spot-capacity-smooth-price-changes-instance-hibernation/]hybernation[/url] is a thing now.

Dubslow 2017-11-29 22:50

Keep in mind a 1090T is literally 6.5 year old technology at this point, and further, even its contemporary Intel processors (Sandy Bridge) were noticeably faster with the same instruction sets. A modern AMD Zen or Intel... whatever-Lake they're on now should be noticeably faster, perhaps even up to an order of magnitude, even if you exclude any new instruction sets from being used.

GP2 2018-03-01 03:59

The 321st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7313983[/M]. It is a semprime.

Congratulations to Oliver Kruse. This is a new record for Mersenne cofactors.

paulunderwood 2018-03-01 09:03

Congrats Oliver :toot:

FWIW, here is my verification:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^7313983-1)/305492080276193" | ../../coding/gwnum/lucasPRP - 1 2 7313983 -1

Lucas testing on x^2 - 9*x + 1 ...
Is Lucas PRP!

real 140m38.679s
user 517m9.572s
sys 16m21.860s
[/CODE]

GP2 2018-03-25 00:05

The 322nd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2789[/M].

Oliver Kruse ran the PRP test, but it was James Hintz who found the most recent factor (44 digits, 144 bits).

Needs a Primo certification from someone, check [URL="http://factordb.com/index.php?id=1100000001112630596"]this FactorDB link[/URL] to see if anyone has submitted it yet.

GP2 2018-04-05 00:41

The 323rd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M22193[/M].

I found the most recent factor. For such small assignments, the ECM code of mprime itself does a quick PRP test on the cofactor, and although this doesn't get reported to Primenet, it writes "Cofactor is a probable prime!" to the results.txt file when applicable, which was the case here.

As of this writing, the actual PRP test assignment hasn't completed yet, it's assigned to axn and presumably queued up and will complete almost instantly after it is started.

As usual, someone can call dibs on Primo certification.

Batalov 2018-04-05 01:37

I'll run it.

axn 2018-04-05 04:23

[QUOTE=GP2;484325]As of this writing, the actual PRP test assignment hasn't completed yet, it's assigned to axn and presumably queued up and will complete almost instantly after it is started.[/QUOTE]
And done.

paulunderwood 2018-04-05 11:42

[QUOTE=Batalov;484333]I'll run it.[/QUOTE]

Ya shudda mentioned "ECPP" with your submission and added a link to the certificate in a comment.

:wrong:

Batalov 2018-04-05 14:45

It only makes sense to add ECPP if you are contending for a top-20 spot, (You want to have ECPP record # 10 thousand - be my guest and do it.) "Proof method = Primo" obviously implies it.

In order to have a link you have to wait for factordb to ingest it. It hasn't yet.

paulunderwood 2018-04-05 15:00

[QUOTE=Batalov;484389]It only makes sense to add ECPP if you are contending for a top-20 spot, (You want to have ECPP record # 10 thousand - be my guest and do it.) "Proof method = Primo" obviously implies it.

In order to have a link you have to wait for factordb to ingest it. It hasn't yet.[/QUOTE]

I see the link to FactorDB now.

I disagree about not including the ECPP code with non-top-20 ECPP proofs. For example: When [I]searching[/I] for ECPP proven primes yours will be missing. However, I do like it that you have shared the credit with Gord Palameta.

Batalov 2018-04-05 17:05

You are confusing the proof method (which you obviously have by definition for every number in the UTM database) and the "record" category.
The "record" category is only there to get the candidate submissions eligible for submission.

Adding "ECPP" tag to small numbers is in fact discouraged by the UTM admins.

GP2 2018-07-15 18:01

The 324th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M32611[/M].

It hasn't been PRP tested on Primenet yet, but when I reported the new factor to Factordb, [URL="http://factordb.com/index.php?id=1000000000000032611"]it displayed FF[/URL].

As always, the Primo certification can be done by whoever claims it first.


Edit: actually, the results.txt file reported "Cofactor is a probable prime!" as well. I should have checked that first.

Batalov 2018-07-15 18:46

Will do proof

EDIT: Finished, uploaded and [URL="http://primes.utm.edu/primes/page.php?id=125463"]reported with UTM code c90[/URL].

wedgingt 2018-07-16 05:44

My data has 286 prime exponent Mersenne numbers with prime or SPRP cofactors, which is a bit less, but I have a somewhat different definition of factors for Mersenne numbers than factordb.com uses.


The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored.


The largest in my "completely factored" list are appended.


-- Will



M( 32531 )
M( 35339 )
M( 41263 )
M( 41521 )
M( 41681 )
M( 57131 )
M( 58199 )
M( 63703 )
M( 82939 )
M( 86137 )
M( 86371 )
M( 87691 )
M( 106391 )
M( 130439 )
M( 136883 )
M( 157457 )
M( 173867 )
M( 221509 )
M( 271211 )
M( 271549 )
M( 406583 )
M( 684127 )

GP2 2018-07-16 14:14

For whatever reason, Factordb doesn't record PRPs above around 500k, and there is no way to report them. They list [url="http://factordb.com/index.php?query=M488441"]M488441[/url] as fully factored but not [url="http://factordb.com/index.php?query=M576551"]M576551[/url] or anything higher.

Your list is missing a number of recent discoveries, particularly at the high end. They are indicated in the bold links below.

However, new factors are continually being discovered for exponents of all sizes, each of which could potentially result in a new PRP. So to complete the list you also have to consider exponents smaller than 32531. For instance [M]M2789[/M] was fully factored a few months ago.

The full list is at [url]http://www.mersenne.ca/prp.php[/url], however unlike Factordb or your sourceforge file, only prime exponents are recorded. There are 324 entries. The ones above your threshold of 32531 are listed below:

32531
[B][M]32611[/M][/B]
35339
41263
41521
41681
[B][M]53381[/M][/B]
57131
58199
63703
82939
[B][M]84211[/M][/B]
86137
86371
87691
106391
130439
136883
[B][M]151013[/M][/B]
157457
173867
[B][M]174533[/M][/B]
[B][M]175631[/M][/B]
221509
[B][M]270059[/M][/B]
271211
271549
406583
[B][M]432457[/M][/B]
[B][M]440399[/M][/B]
[B][M]488441[/M][/B]
[B][M]576551[/M][/B]
[B][M]611999[/M][/B]
[B][M]675977[/M][/B]
684127
[B][M]696343[/M][/B]
[B][M]750151[/M][/B]
[B][M]822971[/M][/B]
[B][M]1010623[/M][/B]
[B][M]1168183[/M][/B]
[B][M]1304983[/M][/B]
[B][M]1629469[/M][/B]
[B][M]1790743[/M][/B]
[B][M]2327417[/M][/B]
[B][M]3464473[/M][/B]
[B][M]4187251[/M][/B]
[B][M]4834891[/M][/B]
[B][M]5240707[/M][/B]
[B][M]7080247[/M][/B]
[B][M]7313983[/M][/B]

GP2 2018-07-16 14:30

[QUOTE=wedgingt;491888]The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored.[/QUOTE]

This distinction isn't an issue for Mersenne numbers with prime exponents, since these cannot share factors with one another.

Batalov 2018-07-16 14:51

PRPtop has a subset of these, too: [URL]http://www.primenumbers.net/prptop/searchform.php?form=%282%5En-1%29%2F%3F&action=Search[/URL]
(this search result requires additional filtering before use)

GP2 2018-07-16 15:28

[QUOTE=Batalov;491910]PRPtop has a subset of these, too: [URL]http://www.primenumbers.net/prptop/searchform.php?form=%282%5En-1%29%2F%3F&action=Search[/URL]
(this search result requires additional filtering before use)[/QUOTE]

Unfortunately that site no longer accepts new entries smaller than 30,000 digits, so more recent discoveries such as [M]M53381[/M] and [M]M84211[/M] are not listed.

It does include a handful of Mersenne numbers with non-prime exponents, but those all seem to be old discoveries from more than a decade ago.

Batalov 2018-07-16 18:52

Yes, indeed - there is a self-inflicted gap up to 30,000 decimal digits.

However, there is always a (very remote) chance that someone somewhere is still digging for unusual high PRPs (not to mention NooE) and would submit just to PRPtop. Who knows. I do cross-reference all sites every once in a while.

GP2 2018-10-12 15:01

The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M51487[/M].

The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor.

It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.

paulunderwood 2018-10-12 15:43

[QUOTE=GP2;497937]The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M51487[/M].

The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor.

It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.[/QUOTE]

[CODE]time ./pfgw64 -k -f0 -od -q"(2^51487-1)/57410994232247/17292148963401772464767849635553" | ../../coding/gwnum/hybrid - 1 2 51487 -1

Testing (x + 1)^(n + 1) == 2 + 3 (mod n, x^2 - 3*x + 1)...
Likely prime!

real 0m1.274s
user 0m1.332s
sys 0m0.008s
[/CODE]

VBCurtis 2018-10-12 15:47

May I reserve the Primo run to verify primality of the M51487 cofactor?

GP2 2018-10-12 16:44

[QUOTE=VBCurtis;497940]May I reserve the Primo run to verify primality of the M51487 cofactor?[/QUOTE]

I think you just did, unless anyone objects.

axn 2018-10-12 16:58

[QUOTE=VBCurtis;497940]May I reserve the Primo run to verify primality of the M51487 cofactor?[/QUOTE]

Should easily make it into [url]https://primes.utm.edu/top20/page.php?id=49[/url]

GP2 2018-10-12 17:54

[QUOTE=axn;497947]Should easily make it into [url]https://primes.utm.edu/top20/page.php?id=49[/url][/QUOTE]

Mersenne numbers are the b=2 special cases of generalized repunits (b[SUP]p[/SUP] − 1) / (b − 1).

I compared Chris Caldwell's [URL="https://primes.utm.edu/top20/page.php?id=49"]list of Mersenne PRP cofactors[/URL], where the largest is not quite 20,000 digits, and his [URL="https://primes.utm.edu/top20/page.php?id=16"]list of generalized repunit PRPs[/URL], where the digit lengths go up to 95,000 digits.

The generalized repunit PRPs in the list all have large b, in the thousands or tens of thousands. Nearly all of the primality certificates are by Tom Wu.

Is it somehow generally true that for larger b it is easier to prove primality of (b[SUP]p[/SUP] − 1) divided by some divisor? And perhaps easier to find PRPs in the first place?

However, looking at the [URL="http://www.primenumbers.net/prptop/prptop.php"]Lifchitz list of top PRPs[/URL], however, the top 1 and 2 are Wagstaff (repunit with b=−2), numbers 4, 5, 6, 8 and 14 are Mersenne cofactors (repunit with b=2), number 11 is a repunit PRP with b=−13, number 12 is a repunit PRP with b=5, etc. I don't see any large b bases in the top rankings.

paulunderwood 2018-10-12 19:06

[QUOTE=GP2;497953]Mersenne numbers are the b=2 special cases of generalized repunits (b[SUP]p[/SUP] − 1) / (b − 1).

I compared Chris Caldwell's [URL="https://primes.utm.edu/top20/page.php?id=49"]list of Mersenne PRP cofactors[/URL], where the largest is not quite 20,000 digits, and his [URL="https://primes.utm.edu/top20/page.php?id=16"]list of generalized repunit PRPs[/URL], where the digit lengths go up to 95,000 digits.

The generalized repunit PRPs in the list all have large b, in the thousands or tens of thousands. Nearly all of the primality certificates are by Tom Wu.

Is it somehow generally true that for larger b it is easier to prove primality of (b[SUP]p[/SUP] − 1) divided by some divisor? And perhaps easier to find PRPs in the first place?

However, looking at the [URL="http://www.primenumbers.net/prptop/prptop.php"]Lifchitz list of top PRPs[/URL], however, the top 1 and 2 are Wagstaff (repunit with b=−2), numbers 4, 5, 6, 8 and 14 are Mersenne cofactors (repunit with b=2), number 11 is a repunit PRP with b=−13, number 12 is a repunit PRP with b=5, etc. I don't see any large b bases in the top rankings.[/QUOTE]

The big proven GRUs are done with CHG or KP proof methods where a great deal of finding and proving the factors of N^2-1 is done, whereas the Mersenne cofactors are purely ECPP.

Batalov 2018-10-12 20:29

[QUOTE=GP2;497953]Is it somehow generally true that for larger b it is easier to prove primality of (b[SUP]p[/SUP] − 1) divided by [STRIKE]some[/STRIKE] algebraic divisor? [/QUOTE]
(b[SUP]p[/SUP] − 1) / (b − 1) - 1 = x * (b[SUP]p-1[/SUP] − 1),
so if p-1 is fairly smooth, and some of the cofactors happen to be prime, then you have a path to N-1 proof. Same for N+1.
What we see at the top [url]https://primes.utm.edu/top20/page.php?id=16[/url], are enriched with harder proof methods but if you use [url]https://primes.utm.edu/primes/search.php[/url], and search for Text Comment = Generalized Repunit, Type = all, Maximum number of primes to output = 2000, you will find tons of simple N+-1 proofs, as well.

VBCurtis 2018-10-13 16:38

[QUOTE=VBCurtis;497940]May I reserve the Primo run to verify primality of the M51487 cofactor?[/QUOTE]

It has been a while since I've used Primo; I forgot that it lacks command-line interface, and I have only SSH access to my 40-thread workstation. I should put some time into re-learning Primo usage on smaller inputs before I tackle a multi-month job; unreserving this cofactor.

Batalov 2018-10-13 17:06

[QUOTE=VBCurtis;497996]... unreserving this cofactor.[/QUOTE]
Reserving M51487 cofactor. Should be a few weeks to a month.

GP2 2018-10-13 17:38

Has anyone tried the [c]primecert[/c] and [c]primecertexport[/c] functions in recent PARI/GP versions? The documentation says it can create a Primo v. 4 certificate. How does the speed compare with the actual Primo program?

alpertron 2018-10-23 14:18

I was able to configure Bash for Windows to run Primo on Windows 10.

I performed the following steps in Ubuntu 18.04 on Bash for Windows:

1) Install Xming (the X server)
2) Open Bash for Windows
3) Type [FONT="Courier New"]sudo apt-get update[/FONT]
4) Type [FONT="Courier New"]sudo apt-get upgrade[/FONT]
5) Type [FONT="Courier New"]sudo apt-get install gdk-pixbuf2.0-0[/FONT]
6) Type [FONT="Courier New"]sudo apt-get install libgtk2.0-dev[/FONT]
7) Type [FONT="Courier New"]sudo apt-get install xdg-utils[/FONT]
8) Open .bashrc (I used nano), add the following line at the end of this file:
[FONT="Courier New"]export DISPLAY=:0[/FONT] and save it.
9) Download the latest version of Primo and decompress it in a directory that can be seen on Bash for Windows
10) Close Bash for Windows
11) Ensure that Xming is running
12) Open Bash for Windows
13) Run Primo and enjoy.

paulunderwood 2018-11-05 02:38

[QUOTE=Batalov;498000]Reserving M51487 cofactor. Should be a few weeks to a month.[/QUOTE]

Congrats for the proof. [url]https://primes.utm.edu/primes/page.php?id=125757[/url]

Batalov 2018-11-05 04:55

Due to factordb bug I cannot upload the cert just yet, but I will this week.

GP2 2019-01-16 14:15

The 326th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3203[/M].

The most recent factor was found by James Hintz, and the PRP test was completed first by M91088807.

axn 2019-01-16 17:44

[QUOTE=GP2;506114]The 326th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3203[/M].

The most recent factor was found by James Hintz, and the PRP test was completed first by M91088807.[/QUOTE]

It is proven in factordb

Madpoo 2019-01-17 05:07

[QUOTE=axn;506133]It is proven in factordb[/QUOTE]

Okay, if I understand the drill this time, I marked that in the database as the cofactor being proven prime. It won't show up in the ECM progress report anymore as needing more curves. :smile:

ATH 2019-01-17 06:14

[QUOTE=GP2;506114]The most recent factor was found by James Hintz, and the PRP test was completed first by M91088807.[/QUOTE]

Interesting username maybe he/she knows something about this exponent? :smile:
[url]https://mersenne.org/M91088807[/url]

GP2 2019-01-17 16:04

[QUOTE=Madpoo;506188]Okay, if I understand the drill this time, I marked that in the database as the cofactor being proven prime. It won't show up in the ECM progress report anymore as needing more curves. :smile:[/QUOTE]

Certification of primality is only feasible for exponents up to around 80k.

Even if a cofactor is merely PRP, it still makes no sense to look for any further factors.

GP2 2019-02-09 03:10

The 327th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3089[/M].

The most recent factor was found by James Hintz, and the PRP test on Primenet is still pending, but [URL="http://factordb.com/index.php?query=2%5E3089-1"]FactorDB[/URL] already shows it as FF (fully-factored).

axn 2019-02-09 05:01

[QUOTE=GP2;508094][URL="http://factordb.com/index.php?query=2%5E3089-1"]FactorDB[/URL] already shows it as FF (fully-factored).[/QUOTE]
And... now proven.

GP2 2019-02-16 22:55

The 328th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M6679[/M].

The most recent (and also first) factor was found by James Hintz, and the PRP test on Primenet was done by Anonymous. The cofactor is already [URL="http://factordb.com/index.php?id=1100000001249511272"]certified prime on FactorDB[/URL].

This is a semiprime, and its exponent p = 3 mod 4.

So this continues the curious empirically observed tendency that exponents of known Mersenne primes are predominantly 1 mod 4 but exponents of known Mersenne semiprimes are predominantly 3 mod 4. And for Wagstaff primes and Wagstaff semiprimes, the tendency is the opposite.

GP2 2019-02-17 00:04

[QUOTE=GP2;508760]This is a semiprime, and its exponent p = 3 mod 4.[/QUOTE]

It is also p = 7 mod 8.

Among Mersenne semiprimes that are sufficiently large (say, p > 1000) or sufficiently asymmetric (say, the smaller factor has bit length less than 5 percent of the overall bit length), there is an empirically observed tendency that the 3 mod 4 exponents are predominantly 7 mod 8 rather than 3 mod 8. However, the statistics are probably too small to be significant. Applying the same filtering produces the opposite tendency in Wagstaff semiprimes.

See for instance [URL="https://mersenneforum.org/showthread.php?p=503584&postcount=84"]this thread[/URL].

GP2 2019-04-05 19:47

The 329th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2357[/M].

The 62-digit factor was found by Ryan Propper, and the PRP test on Primenet was done by matzetoni. The cofactor will no doubt soon be [URL="http://factordb.com/index.php?id=1100000001282024818"]certified prime on FactorDB[/URL].

This is a semiprime, and its exponent p = 1 mod 4.

Batalov 2019-04-06 02:57

2357 is a pretty prime number itself. [SPOILER](2, 3, 5, 7, you know)[/SPOILER]
So it is doubly nice to have M2357 factored! Congrats, Ryan!

axn 2019-04-06 05:15

[QUOTE=GP2;512799]The cofactor will no doubt soon be [URL="http://factordb.com/index.php?id=1100000001282024818"]certified prime on FactorDB[/URL].[/QUOTE]

Well, it is now...

srow7 2019-04-06 07:38

something is wrong with the status of M2357.
F-ECM (factored)
P-PRP (probable prime) ?????
C-LL(verified)

[QUOTE]

[url]https://www.mersenne.org/report_exponent/?exp_lo=2357&exp_hi=&full=1[/url]

2019-04-05 ATH P-PRP M2357 is a probable prime.
2019-04-05 matzetoni P-PRP M2357/66747193058349253980250138299492944283449631375464079700189511 is a probable prime.
2019-04-05 Ryan Propper F-ECM Factor: 66747193058349253980250138299492944283449631375464079700189511
[/QUOTE]

ATH 2019-04-06 08:59

I did use the factor in the worktodo line, so it is:
M2357/66747193058349253980250138299492944283449631375464079700189511
that is PRP, but not sure why the history is wrong.

Dr Sardonicus 2019-04-06 13:27

Congrats on completing another factorization! Something on the factordb page piqued my curiosity:

[quote]Bases checked 5, 7, 11, 13, 125, 127[/quote]
It seemed weird that 125 was selected as a base, seeing as how the base 5 was checked, and 125 = 5^3.

Batalov 2019-04-06 13:54

FDB allows users to manually check in any base (one just types in the "base" and the server runs it). Running funny bases, like 91 or 35 is not a faux pas per se. But 125 _after_ 5, - yeah, that's a bit silly.

Madpoo 2019-04-06 21:43

[QUOTE=ATH;512843]I did use the factor in the worktodo line, so it is:
M2357/66747193058349253980250138299492944283449631375464079700189511
that is PRP, but not sure why the history is wrong.[/QUOTE]

It's not wrong, it's just not displaying everything. :smile:

There is a frustrating amount of variations on how the JSON data was being formatted. Between the different builds of Prime95 and also gpuOwl, there was never really any agreement ahead of time on how it should look, so I've been playing catch-up with it.

For instance, the known factors may show up as a JSON array, or maybe as a value of comma separated numbers. Or maybe upper or lower case, or maybe it's another level deep, etc. LOL

George has settled on a (hopefully) final format in the latest builds of P95 but until we get the first example of something, I'm never really sure what it's going to look like.

Now that I see what a PRP looks like for a cofactor test, I can update the code that makes the raw result look pretty for the website. It did indeed change from:
[QUOTE]"known-factors":"66747193058349253980250138299492944283449631375464079700189511"[/QUOTE]
to:
[QUOTE]"known-factors":["66747193058349253980250138299492944283449631375464079700189511"][/QUOTE]

Which is quite different. I had to go through the same thing with a non-prime result for cofactor PRP so it won't take me long to implement the new variation. :smile:

GP2 2019-04-06 23:56

The 330th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M78737[/M].

The 29-digit factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by ATH.

If certified prime, the [URL="http://factordb.com/index.php?id=1100000001282415963"]cofactor[/URL] would be a new record for Mersenne cofactors, beating the current [M]M63703[/M]. However it would still be smaller than the Wagstaff prime with exponent 83339.

petrw1 2019-04-08 03:43

Lightning strikes twice
 
[QUOTE=GP2;512799]The 329th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2357[/M].

The 62-digit factor was found by Ryan Propper, and the PRP test on Primenet was done by matzetoni. The cofactor will no doubt soon be [URL="http://factordb.com/index.php?id=1100000001282024818"]certified prime on FactorDB[/URL].

This is a semiprime, and its exponent p = 1 mod 4.[/QUOTE]

2557 Factored 92006001376648044276967530077499930523710420381051263551
2019-04-07 Ryan Propper F-ECM
Factor: 92006001376648044276967530077499930523710420381051263551

paulunderwood 2019-04-08 04:28

[QUOTE=GP2;512921]The 330th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M78737[/M].

The 29-digit factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by ATH.

If certified prime, the [URL="http://factordb.com/index.php?id=1100000001282415963"]cofactor[/URL] would be a new record for Mersenne cofactors, beating the current [M]M63703[/M]. However it would still be smaller than the Wagstaff prime with exponent 83339.[/QUOTE]

:toot: My test of Neils' find:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^78737-1)/23714605956035916529/67059801476528402969297162417" | ../../coding/gwnum/lucasPRP - 1 2 78737 -1

Lucas testing on x^2 - 3*x + 1 ...
Is Lucas PRP!

real 0m2.558s
user 0m2.200s
sys 0m0.008s
[/CODE]

Batalov 2019-04-08 06:52

[QUOTE=petrw1;513034]2557 Factored 92006001376648044276967530077499930523710420381051263551
2019-04-07 Ryan Propper F-ECM [/QUOTE]
...but disbelievers (that it is fully factored) are not fools

mathwiz 2019-04-08 19:50

[QUOTE=GP2;512921]The 330th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M78737[/M].

The 29-digit factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by ATH.

If certified prime, the [URL="http://factordb.com/index.php?id=1100000001282415963"]cofactor[/URL] would be a new record for Mersenne cofactors, beating the current [M]M63703[/M]. However it would still be smaller than the Wagstaff prime with exponent 83339.[/QUOTE]

Is anyone working on a prime certification of the cofactor, with Primo (I'm guessing) or some other tool?

paulunderwood 2019-04-08 20:02

[QUOTE=mathwiz;513140]Is anyone working on a prime certification of the cofactor, with Primo (I'm guessing) or some other tool?[/QUOTE]

The trouble with certifying with Primo is that it takes several months and there is no coordination so that people are not stepping on each other's toes. This happened with Peter Kaiser and me with a 29k proof of a Lucas number. As it happened, I took Peter's partially finished work and ran it on my faster computer and we shared the credit. Perhaps a Primo reservation thread might be in order!

srow7 2019-04-13 20:24

2377
[QUOTE]
[url]https://www.mersenne.org/report_exponent/?exp_lo=2377&exp_hi=&full=1[/url]
[/QUOTE]
ryan strikes again
what is the secret ?

petrw1 2019-04-13 20:41

[QUOTE=srow7;513630]2377

ryan strikes again
what is the secret ?[/QUOTE]

This puts us over 95% up to 10,000

paulunderwood 2019-04-13 22:59

[QUOTE=srow7;513630]2377

ryan strikes again
what is the secret ?[/QUOTE]

Ryan has one of these:

:primenet:

petrw1 2019-04-21 06:05

5 for Ryan
 
[url]https://www.mersenne.org/report_exponent/?exp_lo=4159&full=1[/url]

4159 Factored 31268686049852386409057899188977231895225891280471760041

2019-04-21 Ryan Propper F-ECM Factor: 31268686049852386409057899188977231895225891280471760041

GP2 2019-04-28 13:21

The 331st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M15359[/M].

The latest factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by Anonymous.

[URL="http://factordb.com/index.php?id=1100000001291109700"]FactorDB link[/URL]

paulunderwood 2019-04-28 21:37

[QUOTE=GP2;514999]The 331st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M15359[/M].

The latest factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by Anonymous.

[URL="http://factordb.com/index.php?id=1100000001291109700"]FactorDB link[/URL][/QUOTE]

:toot: Congrats to Niels. An easy ECPP for someone.

axn 2019-04-29 09:37

[QUOTE=paulunderwood;515046]An easy ECPP for someone.[/QUOTE]

Yep. :smile:

GP2 2019-04-30 05:31

The 332nd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M4111[/M].

This is a semiprime. The 56-digit factor was found by Ryan Propper, and the PRP test on Primenet was done by ATH.

[URL="http://factordb.com/index.php?id=1100000001291662662"]FactorDB link[/URL]

SethTro 2019-06-12 07:46

Ryan has been exterminating these small exponents!

GP2 2019-08-12 06:33

The 333rd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3637[/M].

The 48-digit factor was found by James Hintz, and Niels_Mache_Nextcloud was assigned the PRP test.

[URL="http://factordb.com/index.php?id=1100000001342901609"]FactorDB link[/URL]

Fun fact: the PRP cofactor is exactly 1000 digits long.

GP2 2019-09-16 21:10

The 334th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3413[/M].

The 43-digit factor was found by Alex Kruppa and the PRP test was done by mnd9.

[URL="http://factordb.com/index.php?id=1100000001359488027"]FactorDB link[/URL]

wedgingt 2019-09-20 03:47

I verified this certificate - for M3413 - just now.


In my data as of the 15th, there are 261 prime exponent Mersenne numbers that are
fully factored, all factors and cofactors proven prime, and 25 prime exponent Mersennes
that are fully factored, the cofactors not proven prime but SPRP to 20+ bases.


Slightly older data is available at the mers project on Sourceforge:


[url]https://sourceforge.net/projects/mers/[/url]


... and:


[url]https://mers.sourceforge.io/mersenne.html[/url]


I have recently started downloading data from factordb.com to compare with my data
and have found several factors it had that I didn't and vice-versa thru M16328, but it
will take some time - years - to compare all of the factordb.com data with mine since
even downloading data for only one exponent every two minutes sometimes hits their
web server's hourly CPU time limit.


I have been downloading data from mersenne.org (GIMPS) for some years now, which
only takes three weeks or so.


-- Will

ATH 2019-09-20 05:20

[QUOTE=wedgingt;526166]In my data as of the 15th, there are 261 prime exponent Mersenne numbers that are
fully factored, all factors and cofactors proven prime, and 25 prime exponent Mersennes
that are fully factored, the cofactors not proven prime but SPRP to 20+ bases.[/QUOTE]

Here is the list of the 293 proven + 41 PRP = 334 (probably) fully factored exponents:
[url]https://www.mersenne.ca/prp.php[/url]

wedgingt 2019-09-20 06:08

Thank you, ATH; I'll add those to my data.


I was downloading from mersenne.ca automatically at one point, but it was too
much traffic for the web server; I may have time soon to try again.


-- Will

S485122 2019-09-20 07:10

[QUOTE=wedgingt;526166]...
I have recently started downloading data from factordb.com ... but it will take some time - years - to compare all of the factordb.com data with mine since even downloading data for only one exponent every two minutes sometimes hits their web server's hourly CPU time limit.

I have been downloading data from mersenne.org (GIMPS) for some years now, which only takes three weeks or so.

-- Will[/QUOTE][QUOTE=wedgingt;526170]...
I was downloading from mersenne.ca automatically at one point, but it was too much traffic for the web server; I may have time soon to try again.

-- Will[/QUOTE]Shouldn't you ask the maintainers of those sites for an export of the data you need : they should be able to give you one of more files to download. (And be willing too since it would prevent their servers being killed by too many queries or using all their allocated bandwidth too quickly :-)

Jacob

wedgingt 2019-09-20 09:08

[QUOTE=S485122;526173]Shouldn't you ask the maintainers of those sites for an export of the data you need : they should be able to give you one of more files to download. (And be willing too since it would prevent their servers being killed by too many queries or using all their allocated bandwidth too quickly :-)

Jacob[/QUOTE]


Yeah, it's on my list of things to do ... but I'm still catching up with other things,
including improving and documenting the mers package that I've maintained
on and off for 30+ years now - I joined GIMPS _very_ early.


-- Will

wedgingt 2019-09-20 09:12

[QUOTE=ATH;526169]Here is the list of the 293 proven + 41 PRP = 334 (probably) fully factored exponents:
[URL]https://www.mersenne.ca/prp.php[/URL][/QUOTE]


I've now written a Perl script to convert the text format download of this page
into the mers format I've been using for 30 years and these are the only
listed factors I didn't already have as of a few days ago.


My next update will, of course, include them and that the cofactors are at least SPRP.



-- Will



M( 3413 )C: 1801386698628063669444450416074615884859831
M( 151013 )C: 61157791169561859593299975690769
M( 174533 )C: 193594572654550537
M( 174533 )C: 91917886778031629891960890057
M( 175631 )C: 92733169
M( 175631 )C: 330463093135534238072561
M( 270059 )C: 540119
M( 270059 )C: 6481417
M( 270059 )C: 7124976157756725967
M( 2327417 )C: 23915387348002001
M( 3464473 )C: 604874508299177
M( 4187251 )C: 72234342371519
M( 4834891 )C: 1701881633
M( 4834891 )C: 70659688575577
M( 5240707 )C: 75392810903
M( 7080247 )C: 156822217506727
M( 7080247 )C: 11283326312536321
M( 7080247 )C: 9632940548330339593
M( 7313983 )C: 305492080276193

James Heinrich 2019-09-20 11:42

[QUOTE=wedgingt;526170]I was downloading from mersenne.ca automatically at one point, but it was too much traffic for the web server; I may have time soon to try again.[/QUOTE]Please send me an email (james@mersenne.ca) and I will provide you direct download links of whatever data you want in the format most useful to you. Makes a lot more sense than you hammering my webserver to try and prise out the data you want from an HTML report. :smile:

GP2 2019-09-22 17:40

The 335th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3037[/M].

The 50-digit most recent factor was found by Ryan Propper and the PRP test was done by mnd9.

[URL="http://factordb.com/index.php?id=1100000001361953237"]FactorDB link[/URL]

wedgingt 2019-09-23 20:04

Downloading from mersenne.ca
 
[QUOTE=James Heinrich;526178]Please send me an email (james@mersenne.ca) and I will provide you direct download links of whatever data you want in the format most useful to you. Makes a lot more sense than you hammering my webserver to try and prise out the data you want from an HTML report. :smile:[/QUOTE]


Thanks; I sent you email just now. Let me know, of course, if there's anything else you'd like to know.

GP2 2019-10-11 15:40

The 336th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2441[/M].

The 49-digit most recent factor was found by Ryan Propper and the PRP test was done by mnd9.

The cofactor has already been certified prime:

[URL="http://factordb.com/index.php?id=1100000001370625023"]FactorDB link[/URL]


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