M12829 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	2,316.1523	79.1045%	1000000	3910366209750	60.9259	13.2611%	2,377.0782	81.8755%	2.7710%
PrimeNet	2⁴⁰	0.0000	65.0000%	500	10000	0.0000	3.2882%	0.0000	66.1509%	1.1509%
GPU72	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.3639%	0.0002	68.6158%	0.4340%
Difference	+23	+2,316.1521	+10.9227%	+999500	+3910366199750	+60.9259	+11.8972%	+2,377.0780	+13.2597%	+13.2597%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12829	76871369	8	26.196	2996 2² × 7 × 107	-	7	107	1.149e-9	3.560e-9	4.074e-9
12829	84519607273	11	36.299	3294084 2² × 3 × 277 × 991	2008-08-26	277	991	7.173e-7	9.034e-8	1.612e-7
12829	16081182682626412318795617019337	32	103.665	626751215317889637493008692 2² × 61 × 71 × 547 × 2129711461 × 31055527849	2012-08-27	2129711461	31055527849	1.381e+13	1.0597	1.2395
12829	1733991250431959462511920452114954081	37	120.384	67580920197675557818688925563760 2⁴ × 3⁴ × 5 × 10429154351493141638686562587	2021-09-15	81	10429154351493141638686562587	1.339e+13	1.625e+17	3.035e+17

exponent	prime factors	composite factor	digits	bits*
12829	76871369 84519607273	6497137918417866737	19	62.495
12829	76871369 16081182682626412318795617019337	1236182527952584830504283511476134662353	40	129.861
12829	84519607273 16081182682626412318795617019337	1359175244820952969361574826828078086838001	43	139.964
12829	76871369 1733991250431959462511920452114954081	133294281254726565235795503973175465578606889	45	146.579
12829	84519607273 1733991250431959462511920452114954081	146556259501327405379363682693772521176548631113	48	156.682
12829	76871369 84519607273 16081182682626412318795617019337	10448166178029681463943931293421229017413801809336 9	51	166.160
12829	76871369 84519607273 1733991250431959462511920452114954081	11265980303386294968729650637551901477422783968732 303697	56	182.878
12829	16081182682626412318795617019337 1733991250431959462511920452114954081	27884630068272145007827118571531849134931508371286 118961609844064297	68	224.049
12829	76871369 16081182682626412318795617019337 1733991250431959462511920452114954081	21435296874066432513181863199189776701036507697357 24255275807157099034412593	76	250.245
12829	84519607273 16081182682626412318795617019337 1733991250431959462511920452114954081	23567979823232488737468555727450766468958958732946 14644551622584165152600832081	79	260.347
12829	76871369 84519607273 16081182682626412318795617019337 1733991250431959462511920452114954081	18117028735762594145262894732219312985681711626160 7568054131619216093002519872605588889	87	286.543

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-05T23:25:53	Jocelyn Larouche	Manual testing	1000000	3910366209750		-	skipped known factor: 76871369 skipped known factor: 84519607273	-	-	60.93	-	-	13.261%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T19:58:00	ANONYMOUS	Manual testing	?	?	84519607273	36.299	11	3.70698e-9	1.53416e-5	2.24772e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.075 GHz-days
Estimated T-Level:	36.428

Digits	B1	Curves	Complete	FacMiss
20	11000	3454 / 100	34.540	0.000%
25	50000	3454 / 280	12.336	0.000%
30	250000	3306 / 640	5.166	0.569%
35	1000000	2761 / 1580	1.747	17.412%
40	3000000	1342 / 4700	0.286	75.159%

New Calculation Method

Total ECM effort:	26.075 GHz-days
Estimated T-Level:	36.428

Digits	B1	Complete	FacMiss
20	11000	521.722	0.000%
25	50000	111.599	0.000%
30	250000	19.493	0.000%
35	1000000	2.778	6.218%
40	3000000	0.332	71.758%
45	11000000	0.034	96.611%
50	44000000	0.003	99.682%

ECM Summary

B1	B2	factor	curves	GHz-days
		16081182682626412318795617019337	1	0.00000e+0
50000	5000000		148	0.030
250000	25000000		520	0.535
500000	50000000		25	0.051
1000000	100000000		1,419	5.839
3000000	300000000		342	4.222
3000000	528000000		921	14.18
3000000	528000000	1733991250431959462511920452114954081	79	1.216

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-07T15:38:00	Matthias Wurtinger	AMD_Funzel	50000	5000000						50	0.010
2009-06-07T05:09:00	unconnected	dual5430	250000	25000000						30	0.031
2009-06-08T03:30:00	Rob_Dee	twopc	50000	5000000						80	0.016
2009-07-09T01:47:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-10T06:13:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-10T21:28:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-11T01:09:00	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-13T19:07:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-14T09:18:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-15T19:50:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-16T16:35:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-17T14:31:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-19T07:11:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-21T12:09:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-22T22:55:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-24T02:54:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-26T23:21:00	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-30T02:27:00	Rob_Dee	twopc	500000	50000000						5	0.010
2009-07-31T00:55:00	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-05T01:44:00	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-12T15:05:00	Rob_Dee	twopc	500000	50000000						5	0.010
2009-09-03T22:40:00	Rob_Dee	twopc	500000	50000000						5	0.010
2011-01-12T16:47:00	BloodIce	Mjolnir	250000	25000000						96	0.099
2011-01-12T22:57:00	BloodIce	Mjolnir	250000	25000000						18	0.019
2011-04-11T20:18:00	James Hintz	17_051310	250000	25000000						11	0.011
2012-08-21T21:26:00	BloodIce	Mjolnir4	250000	25000000						100	0.103
2012-08-22T07:38:00	BloodIce	Mjolnir4	250000	25000000						100	0.103
2012-08-22T08:26:00	BloodIce	Mjolnir4	250000	25000000						65	0.067
2012-08-27T11:12:00	BloodIce	URM2			16081182682626412318795617019337	103.665		1		1	-
2012-08-27T18:16:00	BloodIce	URM2	1000000	100000000						50	0.206
2012-08-27T18:18:00	BloodIce	URM2	1000000	100000000						50	0.206
2012-08-27T18:40:00	BloodIce	URM2	1000000	100000000						50	0.206
2012-08-28T01:39:00	BloodIce	URM2	1000000	100000000						50	0.206
2017-04-19T11:08:45	kkmrkkblmbrbk	c4.large	1000000	100000000						1219	5.016
2019-02-03T18:00:14	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-02-05T14:32:49	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-07T12:15:03	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-09T08:53:03	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-11T07:11:56	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-13T04:09:45	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-02-15T01:29:22	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-16T23:19:07	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-02-18T20:36:12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-02-20T18:29:49	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-22T16:08:14	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-02-24T14:19:16	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-02-26T11:36:50	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-02-28T09:37:45	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-02T06:57:11	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-04T03:09:59	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-06T01:19:23	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-07T20:22:26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-08T20:49:01	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-10T03:54:24	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-11T19:11:19	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-13T13:51:09	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-15T10:55:23	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-18T10:43:31	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-20T13:15:26	storm5510	3570_Ivy_Bridge	3000000	300000000						3	0.037
2019-03-22T11:45:26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-24T18:28:32	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-27T01:24:31	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-28T23:00:57	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-30T21:12:37	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-01T18:21:10	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-03T17:14:50	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-05T15:02:36	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-07T12:02:14	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-09T10:37:38	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-11T09:26:28	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-13T23:22:40	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-17T08:05:10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-20T17:54:26	storm5510	HP-Z220-CMT	3000000	300000000						3	0.037
2019-04-23T22:16:09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-25T19:08:11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-27T14:56:03	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-29T16:38:23	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-05-02T17:50:13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-05T00:34:18	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-07T09:51:07	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-10T00:01:49	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-12T08:21:54	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-14T03:22:12	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-15T20:40:56	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-19T03:41:45	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-22T14:44:49	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-26T03:12:47	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-29T16:07:21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-02T08:08:32	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-05T19:24:31	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-09T08:24:54	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-12T22:09:58	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-16T11:05:35	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-19T22:10:47	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-23T11:15:48	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-27T01:33:48	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-07-02T19:05:07	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-16T07:35:30	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-22T10:59:51	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-24T18:30:12	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-27T01:08:27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-29T08:03:35	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-31T17:15:06	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-02T22:51:54	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-05T06:16:27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-07T12:50:54	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-09T19:07:13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-12T00:11:32	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-14T06:00:03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-16T14:08:03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-18T22:36:16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-21T05:01:34	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-23T11:13:35	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-25T18:29:16	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-28T01:46:13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-30T09:03:39	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-01T15:31:49	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-03T23:21:07	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-06T04:42:07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-08T13:44:02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-10T21:55:40	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-13T05:35:55	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-15T12:16:51	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-17T19:53:41	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-20T04:43:48	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-22T11:49:54	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-24T20:00:02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-27T05:16:04	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-29T10:29:00	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-01T18:12:26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-04T03:00:01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-06T09:48:48	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-08T16:20:34	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-11T00:14:52	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-13T08:51:59	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-15T16:04:07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-18T01:26:44	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-20T07:26:45	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-22T14:38:34	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-24T23:15:33	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-27T06:31:51	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-29T13:53:54	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-31T19:44:42	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-03T02:03:09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-05T07:27:23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-07T14:26:22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-09T20:33:11	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-12T03:02:11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2021-09-15T11:48:09	nordi	sweet16	3000000	528000000	1733991250431959462511920452114954081	120.384	79	2	836948325433098	79	1.216
2021-09-20T07:46:06	nordi	sweet16	3000000	528000000						921	14.18

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