M31393 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	946.5141	77.6119%	12000000000	1000658212433880	43,553.5383	33.3485%	44,500.0524	85.0780%	7.4661%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1512%	0.0000	64.0567%	1.5567%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7822%	0.0001	66.5167%	0.6076%
Difference	+23	+946.5140	+11.7028%	+11999999500	+1000658212423880	+43,553.5383	+31.5663%	+44,500.0523	+18.5614%	+18.5614%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-29T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.001	-	-	1.965%
2001-08-18T00:00:00	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.005	-	-	4.779%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	8.36694e-5	-	-	0.658%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.000	-	-	1.058%
2002-07-20T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.583%
2003-02-02T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.001	-	-	2.233%
2003-03-27T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	3.000%
2003-04-03T00:00:00	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.003	-	-	3.875%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.005	-	-	4.848%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.011	-	-	5.914%
2003-07-13T00:00:00	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.021	-	-	7.064%
2003-10-08T00:00:00	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.043	-	-	8.293%
2003-10-08T00:00:00	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.086	-	-	9.583%
2013-11-09T05:55:00	David Campeau	i5-2500k	207835000	11015255000		-		-	-	0.636	-	-	13.576%
2017-04-03T21:27:33	nordi	nordiputer	2756919005	181956654341	12	-		-	-	10.00	-	-	19.049%
2022-04-23T13:08:29	ATH	Manual testing	12000000000	1000658212433880		-		-	-	43,554	-	-	33.348%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-05-07T18:46:02	ATH	5960X	500000000	101500000000	2	7			-	-	4.914

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-10-29T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.019	-	-
2000-03-08T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.038	-	-
2000-09-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.306	-	-
2002-12-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.612	-	-
2016-02-23T04:50:49	LaurV	Manual testing	2⁵⁷	2⁵⁸		-	-	0.612	-	-
2009-01-07T22:06:00	Sturle Sunde	hoffman.ifi	2⁵⁸	2⁵⁹		-	-	1.223	-	-
2009-02-07T00:47:00	Sturle Sunde	gerle.ifi	2⁵⁹	2⁶⁰		-	-	2.446	-	-
2012-03-23T02:13:00	bcp19	Manual testing	2⁶⁰	2⁶¹		-	-	4.892	-	-
2012-03-23T02:13:00	bcp19	Manual testing	2⁶¹	2⁶²		-	-	9.78	-	-
2016-11-22T08:54:21	Sid & Andy	Woody	2⁶²	2⁶³		-	-	31.27	-	-
2018-06-05T16:30:04	Yxinity	Manual testing	2⁶³	2⁶⁴		-	-	62.54	-	-
2018-06-05T11:21:54	Yxinity	YGSMainFrame	2⁶³	2⁶⁴		-	-	62.54	-	-
2019-12-08T10:48:33	Yxinity	Manual testing	2⁶⁴	2⁶⁵		-	-	119.0	-	-
2019-12-08T04:53:32	Yxinity	YGSMainFrame	2⁶⁴	2⁶⁵		-	-	119.0	-	-
2020-12-30T09:14:20	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	238.0	-	-
2020-12-29T23:56:30	Yxinity	YGSMainFrame	2⁶⁵	2⁶⁶		-	-	238.0	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	280.061 GHz-days
Estimated T-Level:	40.571

Digits	B1	Curves	Complete	FacMiss
20	11000	5343 / 100	53.430	0.000%
25	50000	5343 / 280	19.082	0.000%
30	250000	5343 / 640	8.348	0.024%
35	1000000	5343 / 1566	3.412	3.294%
40	3000000	5112 / 4588	1.114	32.813%
45	11000000	1050 / 9201	0.114	89.215%

New Calculation Method

Total ECM effort:	280.061 GHz-days
Estimated T-Level:	40.571

Digits	B1	Complete	FacMiss
20	11000	1,121.733	0.000%
25	50000	318.163	0.000%
30	250000	67.605	0.000%
35	1000000	11.681	0.001%
40	3000000	1.709	18.099%
45	11000000	0.219	80.309%
50	44000000	0.025	97.528%
55	110000000	0.003	99.741%

ECM Summary

B1	B2	curves	GHz-days
1000000	100000000	231	2.655
3000000	300000000	4,012	138.3
5000000	500000000	50	2.873
11000000	1100000000	950	120.1
11000000	2024000000	100	16.10

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05T05:34:00	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-05T08:00:00	Sturle Sunde	v17	1000000	100000000						3	0.034
2009-04-06T19:29:00	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-07T08:24:00	Sturle Sunde	v17	1000000	100000000						3	0.034
2009-04-07T23:45:00	Sturle Sunde	v22	1000000	100000000						3	0.034
2009-04-08T12:53:00	Sturle Sunde	v17	1000000	100000000						3	0.034
2009-04-09T14:58:00	Sturle Sunde	v22	1000000	100000000						3	0.034
2009-04-10T02:08:00	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-10T23:07:00	Carsten Kossendey	durandal	1000000	100000000						1	0.011
2009-04-11T00:01:00	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-16T17:05:00	Sparky70	Laptop2200	1000000	100000000						3	0.034
2009-05-02T02:02:00	unconnected	saudi-E5405	1000000	100000000						100	1.149
2009-06-26T10:19:00	unconnected	dual5430-2	3000000	300000000						100	3.448
2009-10-27T07:51:00	GrunwalderGIMP	GWPrime02	1000000	100000000						100	1.149
2010-05-12T19:44:00	James Hintz	OMFG	3000000	300000000						11	0.379
2010-06-16T14:42:00	James Hintz	17_051310	3000000	300000000						11	0.379
2010-09-26T07:58:00	James Hintz	NEW_OMFG	3000000	300000000						5	0.172
2014-01-12T15:20:00	mikr	MSI	3000000	300000000						36	1.241
2014-01-25T14:51:00	mikr	MSI	3000000	300000000						25	0.862
2014-02-10T04:24:00	mikr	MSI	3000000	300000000						41	1.414
2014-10-13T18:09:00	mikr	Dell	3000000	300000000						34	1.172
2015-02-16T21:53:00	mikr	Dell	3000000	300000000						50	1.724
2016-03-03T22:28:06	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-03-07T13:58:43	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-03-09T14:02:26	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-03-11T15:10:07	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-03-16T12:51:11	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-03-18T22:37:02	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-03-28T23:26:55	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-04-01T15:24:48	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-04-06T13:55:00	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-04-13T19:27:40	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-04-23T04:50:39	James Hintz	08_04_2014	3000000	300000000						11	0.379
2016-05-13T18:39:41	James Hintz	04_29_2016	3000000	300000000						11	0.379
2016-06-08T20:39:48	James Hintz	04_29_2016	3000000	300000000						11	0.379
2016-06-15T22:07:34	James Hintz	04_29_2016	3000000	300000000						11	0.379
2016-06-20T09:55:04	volki	Manual testing	3000000	300000000						150	5.172
2017-03-24T16:45:20	James Hintz	alek_07_13_2016	3000000	300000000						100	3.448
2017-04-16T01:46:00	James Hintz	11_04_2016	3000000	300000000						10	0.345
2017-05-22T22:20:37	nordi	nordiputer	3000000	300000000						1000	34.48
2017-06-08T02:47:12	James Hintz	lappy_12_22_2016	3000000	300000000						100	3.448
2017-06-09T06:31:40	James Hintz	lappy_12_22_2016	3000000	300000000						100	3.448
2017-06-19T15:08:15	nordi	nordiputer	3000000	300000000						1000	34.48
2017-07-07T19:14:37	nordi	nordiputer	3000000	300000000						1000	34.48
2018-03-11T21:09:13	lycorn	Nebula	5000000	500000000						50	2.873
2018-04-09T18:52:01	srow7	Manual testing	3000000	300000000						85	2.931
2020-03-11T19:06:23	James Hintz	work_5_9_2019	11000000	1100000000						100	12.64
2020-11-12T22:46:21	nordi	sweet16	11000000	1100000000						100	12.64
2020-11-14T14:33:46	nordi	sweet16	11000000	1100000000						100	12.64
2020-11-16T07:33:11	nordi	sweet16	11000000	1100000000						100	12.64
2020-11-18T00:35:04	nordi	sweet16	11000000	1100000000						100	12.64
2020-11-19T17:56:53	nordi	sweet16	11000000	1100000000						100	12.64
2021-08-19T11:59:08	nordi	sweet16	11000000	2024000000						100	16.10
2022-01-01T14:14:52	GAN	Manual testing	11000000	1100000000						350	44.25

date	userid	compid	res64	spent (GHz-days)
2015-04-11T05:58:00	MadPoo	Manual testing	FC270048FE222853	1.72923e-5

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 12000000000, B2 = 1000658212433880 (P-1 stage 2)

B1 = 2756919005, B2 = 181956654341 (P-1 stage 2)

B1 = 12000000000 (P-1 stage 1)

B1 = 2756919005 (P-1 stage 1)

B1 = 207835000, B2 = 11015255000 (P-1 stage 2)

B1 = 207835000 (P-1 stage 1)

B1 = 16777216, B2 = 1677721600 (P-1 stage 2)

B1 = 8388608, B2 = 838860800 (P-1 stage 2)

B1 = 4194304, B2 = 419430400 (P-1 stage 2)

B1 = 16777216 (P-1 stage 1)

B1 = 2097152, B2 = 209715200 (P-1 stage 2)

B1 = 8388608 (P-1 stage 1)

B1 = 1048576, B2 = 104857600 (P-1 stage 2)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 4194304 (P-1 stage 1)

B1 = 524288, B2 = 52428800 (P-1 stage 2)

B1 = 2097152 (P-1 stage 1)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 1048576 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 524288 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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