M1696451 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	2⁶⁸	35.1350	69.1176%	10000000	200000000	1.3888	9.1065%	36.5239	71.9299%	2.8123%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7302%	0.0123	64.1638%	1.0059%
GPU72	2⁶¹	0.1811	65.5738%	7000	100000	0.0008	1.3007%	0.1819	66.0216%	0.4478%
Difference	+7	+34.9540	+3.5439%	+9993000	+199900000	+1.3880	+7.8057%	+36.3420	+5.9084%	+5.9084%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1696451	77184966618035150445813235651088297	35	115.894	22748952553900805400749339548 2² × 1171 × 385112863 × 12611202345702019	2019-11-02	385112863	12611202345702019	7.836e+10	46,887,687	87,573,096

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-26T23:36:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.488%
2011-02-02T14:16:00	Carsten Kossendey	leela	90000	1485000		-		-	-	0.011	-	-	2.073%
2014-03-31T21:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.765%
2014-05-01T10:19:00	ANONYMOUS	Manual testing	150000	150000		-		-	-	0.010	-	-	0.967%
2014-09-30T23:23:00	Jocelyn Larouche	Manual testing	187834	187834		-		-	-	0.013	-	-	1.093%
2015-01-05T22:25:00	Jocelyn Larouche	Manual testing	281751	281751		-		-	-	0.019	-	-	1.343%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	309926	309926		-		-	-	0.021	-	-	1.407%
2015-02-15T11:05:00	VictordeHollander	Manual testing	10000000	200000000		-		-	-	1.389	-	-	9.106%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:46	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.068	-	-
2010-04-24T12:42:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.091	-	-
2016-02-23T16:28:46	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.181	-	-
2010-09-26T01:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.941	-	-
2016-02-23T16:28:46	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.579	-	-
2015-01-30T19:14:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	1.157	-	-
2015-01-30T19:14:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	2.202	-	-
2015-10-13T10:54:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.405	-	-
2017-09-08T12:43:25	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.810	-	-
2019-06-17T12:15:08	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.62	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.916 GHz-days
Estimated T-Level:	23.411

Digits	B1	Curves	Complete	FacMiss
20	11000	191 / 100	1.910	14.666%
25	50000	191 / 280	0.682	50.492%
30	250000	15 / 640	0.023	97.682%

New Calculation Method

Total ECM effort:	14.916 GHz-days
Estimated T-Level:	23.411

Digits	B1	Complete	FacMiss
20	11000	6.927	0.098%
25	50000	0.694	49.965%
30	250000	0.051	95.018%
35	1000000	0.003	99.693%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		176	10.46
250000	25000000	77184966618035150445813235651088297	15	4.457

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-20T09:36:00	James Heinrich	Q6600	50000	5000000						3	0.178
2009-06-16T10:36:00	James Hintz	11_060902	50000	5000000						3	0.178
2010-06-21T21:13:00	KAMCOBILL	PC01	50000	5000000						3	0.178
2011-11-16T10:08:00	OS1	L3	50000	5000000						3	0.178
2013-04-14T21:54:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-01-02T14:17:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-09-10T11:28:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-01-06T10:10:00	mikr	MSI	50000	5000000						12	0.713
2016-06-04T15:28:10	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2016-09-04T12:08:52	Bruce	DESK3	50000	5000000						3	0.178
2016-11-06T14:54:35	Bruce	DESK3	50000	5000000						3	0.178
2017-01-02T13:43:00	Bruce	DESK3	50000	5000000						3	0.178
2017-04-21T11:10:10	ANONYMOUS	Worker	50000	5000000						3	0.178
2017-10-31T13:55:56	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2018-01-15T21:34:49	Bruce	DESK3	50000	5000000						3	0.178
2019-07-05T04:05:45	storm5510	7700_Kaby_Lake	50000	5000000						3	0.178
2019-11-02T12:07:38	nordi	nordiputer	250000	25000000	77184966618035150445813235651088297	115.894	15	2	8654937224968351	15	4.457
2020-02-03T10:37:56	TJAOI	Manual testing	50000	5000000						119	7.072

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	6364714D269AF90E	0.080
1999-08-31T00:00:00	ANONYMOUS	v4_computers	6364714D269AF90E	0.080
2015-07-03T04:32:00	MadPoo	Manual testing	6364714D269AF90E	0.080

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 = 10000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 309926 (P-1 stage 1)

B1 = 281751 (P-1 stage 1)

B1 = 187834 (P-1 stage 1)

B1 = 90000, B2 = 1485000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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