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-   -   Mersenne number factored (disbelievers are biting elbows) (https://www.mersenneforum.org/showthread.php?t=19407)

Dr Sardonicus 2017-10-20 15:07
[QUOTE=James Heinrich;470125]There are indeed 9 factors for M397, the smallest 8 of which are listed on the [url=http://www.mersenne.ca/exponent/397]exponent page[/url], the last one (6597485910270326519900042655193) is only shown on demand on the [url=http://www.mersenne.ca/prp.php?show=2&min_exponent=0&max_exponent=1000#M397]PRP page[/url].

I have updated the [url=http://www.mersenne.ca/manyfactors.php]many-factors page[/url] to take these kind of PRP last-factors into account, the affected exponents are shown in red.
And yes, in many cases with smaller exponents the percentage-known won't quite reach 100% due to rounding.[/QUOTE]Thanks, the PRP page clearly lists the cases when 2^n - 1 is either fully factored, or the remaining cofactor has been tested as a PRP, but not known to be prime.

The old printed tables usually list the last cofactor as Pxxx, PRPxxx, or Cxxx (proven prime, tested as PRP, or proven composite (i.e. tested as not-PRP) with xxx decimal digits). The only additional notation I can think of offhand is Uxxx, ("unknown" or "untested," for any cases where the remaining cofactor has not been PRP-tested.

GP2 2017-10-27 08:33
The [STRIKE]318th[/STRIKE] 319th 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].

Batalov 2017-10-27 14:37
[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]
Congrats! Submitted under your name to [URL="http://www.primenumbers.net/prptop/prptop.php"]PRP top[/URL]

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:


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