M13669 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	2,173.8179	79.1045%	1000000000	248016220902450	3,864.5009	28.0891%	6,038.3188	84.9738%	5.8694%
PrimeNet	2⁴⁰	0.0000	65.0000%	500	10000	0.0000	3.3442%	0.0000	66.1705%	1.1705%
GPU72	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.3904%	0.0002	68.6242%	0.4424%
Difference	+23	+2,173.8178	+10.9227%	+999999500	+248016220892450	+3,864.5009	+26.6987%	+6,038.3187	+16.3496%	+16.3496%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13669	300719	6	18.198	11 11	-	1	11	2.561e-12	4.418e-10	5.820e-10
13669	956831	6	19.868	35 5 × 7	2008-08-26	5	7	5.148e-12	1.461e-9	2.910e-9
13669	1640281	7	20.646	60 2² × 3 × 5	2008-08-26	4	5	1.035e-11	1.159e-9	2.328e-9
13669	5726507279850970625758280850336071	34	112.141	209470600623709511513581127015 5 × 7 × 19 × 29 × 69004912783 × 157406775883013	2021-09-30	69004912783	157406775883013	1.327e+13	2,471.1	4,580.6

exponent	prime factors	composite factor	digits	bits*
13669	300719 956831	287737261489	12	38.066
13669	300719 1640281	493263662039	12	38.844
13669	956831 1640281	1569471709511	13	40.513
13669	300719 956831 1640281	471969963012438409	18	58.711
13669	300719 5726507279850970625758280850336071	1722069542689504035607404459032212935049	40	130.339
13669	956831 5726507279850970625758280850336071	5479299687087084074814921624307913151001	40	132.009
13669	1640281 5726507279850970625758280850336071	9393081087501229948989418671470100875951	40	132.787
13669	300719 956831 5726507279850970625758280850336071	1647729522601140835894268415940251334855869719	46	150.207
13669	300719 1640281 5726507279850970625758280850336071	2824677951552282369030148993465817265315108769	46	150.985
13669	956831 1640281 5726507279850970625758280850336071	8987591170034889353321494456841408091237071281	46	152.655
13669	300719 956831 1640281 5726507279850970625758280850336071	27027394290617218914414864915668913997887208385510 39	52	170.853

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-12-14T18:21:02	Lisander Viaene	30.8b5	1000000	9113723048430		-	skipped known factor: 300719 skipped known factor: 956831 skipped known factor: 1640281	-	-	142.0	-	-	14.129%
2021-12-14T20:36:04	Lisander Viaene	30.8b5	101101101	78389316415410		-	skipped known factor: 300719 skipped known factor: 956831 skipped known factor: 1640281	-	-	1,221	-	-	23.894%
2022-03-04T09:24:57	Ethan O'Connor	Manual testing	1000000000	248016220902450		-	skipped known factor: 300719 skipped known factor: 956831 skipped known factor: 1640281	-	-	3,865	-	-	28.089%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T19:58:00	ANONYMOUS	Manual testing	?	?	1640281	20.646	7	1.32720e-13	1.63985e-5	8.07323e-13
2008-08-26T19:58:00	ANONYMOUS	Manual testing	?	?	956831	19.868	6	3.87100e-14	1.63985e-5	2.35469e-13

ECM factoring results:

Old Calculation Method

Total ECM effort:	22.423 GHz-days
Estimated T-Level:	36.364

Digits	B1	Curves	Complete	FacMiss
20	11000	3412 / 100	34.120	0.000%
25	50000	3412 / 280	12.186	0.000%
30	250000	3264 / 640	5.100	0.607%
35	1000000	2703 / 1580	1.711	18.063%
40	3000000	1282 / 4700	0.273	76.125%

New Calculation Method

Total ECM effort:	22.423 GHz-days
Estimated T-Level:	36.364

Digits	B1	Complete	FacMiss
20	11000	511.091	0.000%
25	50000	108.899	0.000%
30	250000	18.952	0.000%
35	1000000	2.692	6.775%
40	3000000	0.321	72.563%
45	11000000	0.033	96.730%
50	44000000	0.003	99.694%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		148	0.030
250000	25000000		551	0.567
500000	50000000		10	0.021
1000000	100000000		1,421	5.848
3000000	300000000		1,239	15.30
3000000	528000000	5726507279850970625758280850336071	43	0.662

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-07T19:19:00	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.010
2009-06-07T13:56:00	unconnected	dual5430	250000	25000000						30	0.031
2009-06-09T06:13:00	Rob_Dee	twopc	50000	5000000						80	0.016
2009-07-07T08:41:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07T21:41:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08T00:17:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08T07:20:00	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-09T13:37:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-21T20:08:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-24T14:47:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-28T17:03:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-31T21:22:00	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-10T14:10:00	Rob_Dee	twopc	500000	50000000						5	0.010
2010-06-16T16:50:00	James Hintz	home2	250000	25000000						481	0.495
2010-12-30T23:53:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-09T09:34:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-12T06:16:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-15T01:54:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-18T01:15:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-21T06:12:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-24T13:20:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-27T20:45:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-31T09:22:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-03-31T14:24:00	James Hintz	newestmember	1000000	100000000						3	0.012
2011-04-10T11:54:00	James Hintz	17_051310	1000000	100000000						11	0.045
2017-06-02T12:07:27	kkmrkkblmbrbk	c4.large	1000000	100000000						1380	5.679
2019-02-27T23:56:31	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-01T23:59:04	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-04T00:58:33	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-06T01:46:23	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-07T23:12:14	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-09T00:43:25	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-10T11:45:18	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-12T08:18:40	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-14T07:02:43	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-16T15:52:07	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-19T13:05:22	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-21T14:17:43	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-23T23:42:55	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-26T12:19:30	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-28T13:13:35	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-30T15:20:06	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-01T16:12:03	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-03T18:11:13	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-05T20:04:41	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-07T20:31:45	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-09T22:36:54	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-11T23:45:22	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-15T06:29:44	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-18T20:49:24	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-22T11:00:34	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-25T00:47:27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-27T00:41:57	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-29T03:30:47	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-02T09:49:57	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-04T18:51:39	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-07T08:29:04	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-10T02:16:22	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-12T13:31:31	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-14T10:42:50	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-16T09:35:24	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-20T07:11:40	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-24T00:05:30	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-27T19:39:45	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-31T16:50:51	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-04T11:34:31	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-08T06:41:02	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-12T01:45:00	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-15T20:34:53	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-19T14:23:24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-23T09:47:10	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-27T06:37:13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-07-04T16:10:53	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-19T02:54:03	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-23T02:53:19	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-07-25T13:14:50	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-27T23:53:53	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-30T11:01:28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-01T23:03:22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-04T10:45:10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-06T20:31:17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-09T08:22:51	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-11T17:50:10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-14T02:06:01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-16T14:05:54	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-19T02:02:58	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-21T13:09:33	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-23T23:17:00	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-26T09:38:21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-28T21:10:58	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-31T09:21:01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-02T18:56:25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-05T06:07:57	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-07T18:10:03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-10T05:51:55	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-12T17:45:16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-15T05:45:18	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-17T15:48:41	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-20T06:44:13	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-22T17:17:25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-25T05:32:03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-27T16:50:34	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-30T02:52:10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-02T16:03:09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-05T04:36:49	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-07T14:20:04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-10T01:19:05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-12T14:56:14	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-15T03:28:35	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-17T13:33:25	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-20T00:51:02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-22T12:57:37	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-24T23:29:27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-27T12:27:44	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-30T01:14:15	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-01T09:21:21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-03T19:10:10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-06T05:52:13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-08T14:54:29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-11T01:27:40	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2021-09-30T18:20:33	nordi	sweet16	3000000	528000000	5726507279850970625758280850336071	112.141	43	2	3506642045434585	43	0.662
2021-10-07T15:58:14	nordi	sweet16	3000000	300000000						957	11.81

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront