M2076161 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	28.7092	69.1176%	4000000	200000000	1.3994	8.7713%	30.1086	71.8264%	2.7088%
PrimeNet	2⁵⁸	0.0185	63.7931%	9000	160000	0.0016	2.6720%	0.0201	64.7606%	0.9675%
GPU72	2⁶²	0.2959	66.1290%	9000	130000	0.0015	1.3672%	0.2974	66.5921%	0.4631%
Difference	+6	+28.4133	+2.9886%	+3991000	+199870000	+1.3979	+7.4041%	+29.8112	+5.2343%	+5.2343%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2076161	31840568463089992742234671	26	84.719	7668135675193299735 3 × 5 × 11² × 13 × 324989856969413	2020-07-25	121	324989856969413	2,628,423	1,688,079	3,152,861

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.223%
2009-07-25T11:28:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.875%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.350%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.509%
2011-01-20T20:47:00	James Heinrich	Q6600	135000	3071250		-		-	-	0.028	-	-	2.756%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	165915	165915		-		-	-	0.016	-	-	1.059%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	207393	207393		-		-	-	0.020	-	-	1.191%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	228132	228132		-		-	-	0.022	-	-	1.250%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	250945	250945		-		-	-	0.024	-	-	1.312%
2015-02-02T07:32:00	Jocelyn Larouche	Manual testing	276039	276039		-		-	-	0.026	-	-	1.375%
2015-02-12T12:33:00	Jocelyn Larouche	Manual testing	444560	444560		-		-	-	0.042	-	-	1.717%
2015-02-14T12:30:00	Jocelyn Larouche	Manual testing	537917	537917		-		-	-	0.051	-	-	1.866%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	591708	591708		-		-	-	0.056	-	-	1.943%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	650878	650878		-		-	-	0.062	-	-	2.022%
2015-03-03T20:46:00	Jocelyn Larouche	Manual testing	715965	715965		-		-	-	0.068	-	-	2.103%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	787561	787561		-		-	-	0.075	-	-	2.186%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	866317	866317		-		-	-	0.083	-	-	2.271%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	1048242	1048242		-		-	-	0.100	-	-	2.445%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	1268372	1268372		-		-	-	0.121	-	-	2.627%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	1395209	1395209		-		-	-	0.133	-	-	2.720%
2015-05-22T00:29:00	Jocelyn Larouche	Manual testing	1534729	1534729		-		-	-	0.146	-	-	2.816%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	1688201	1688201		-		-	-	0.161	-	-	2.913%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1857021	1857021		-		-	-	0.177	-	-	3.011%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	2042723	2042723		-		-	-	0.195	-	-	3.112%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	2246995	2246995		-		-	-	0.214	-	-	3.214%
2016-07-07T00:37:33	Jocelyn Larouche	Manual testing	2246995	4493990	6	-		-	-	0.226	-	-	3.991%
2016-09-24T23:31:24	Jocelyn Larouche	low 4M	2246995	8987980	6	-		-	-	0.249	-	-	4.775%
2018-02-23T11:35:54	Jocelyn Larouche	low 4M	2256995	4513990	6	-		-	-	0.227	-	-	3.997%
2019-09-11T06:33:41	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.771%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T08:02:00	Sturle Sunde	homilius.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-16T19:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.148	-	-
2013-09-01T20:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.473	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.946	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.800	-	-
2015-11-05T09:47:16	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.599	-	-
2016-09-10T20:44:41	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.199	-	-
2019-03-29T01:44:37	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.687 GHz-days
Estimated T-Level:	22.036

Digits	B1	Curves	Complete	FacMiss
20	11000	114 / 100	1.140	31.799%
25	50000	114 / 280	0.407	66.506%

New Calculation Method

Total ECM effort:	9.687 GHz-days
Estimated T-Level:	22.036

Digits	B1	Complete	FacMiss
20	11000	3.677	2.529%
25	50000	0.332	71.723%
30	250000	0.020	97.974%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		111	9.432
50000	5000000	31840568463089992742234671	3	0.255

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-11T08:30:00	Smurgs	Praca	50000	5000000						3	0.255
2009-11-01T00:14:00	SubPrime	mysql0	50000	5000000						3	0.255
2011-05-05T08:17:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-15T19:34:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-08-10T19:52:00	he4var		50000	5000000						3	0.255
2015-07-23T19:21:00	nranks	wlaptop	50000	5000000						3	0.255
2016-02-20T11:29:55	Bruce	Desk8	50000	5000000						3	0.255
2016-05-14T22:00:55	lettp	Home	50000	5000000						3	0.255
2016-07-24T17:05:23	Bruce	test	50000	5000000						3	0.255
2017-01-12T01:04:42	Clark B. Wierda	CF-27	50000	5000000						3	0.255
2017-07-31T07:57:08	Clark B. Wierda	CF-27	50000	5000000						3	0.255
2017-12-18T16:34:16	Bruce	Desk6	50000	5000000						3	0.255
2018-05-09T12:20:30	Bruce	Desk6	50000	5000000						3	0.255
2018-10-12T18:03:21	storm5510	7700_Kaby_Lake	50000	5000000						3	0.255
2020-01-01T09:44:35	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-01-06T21:51:04	EricP	Cannonfodder	50000	5000000						3	0.255
2020-01-15T03:20:32	Nesowa	6700T	50000	5000000						3	0.255
2020-01-27T21:34:39	mnd9	75204b	50000	5000000						3	0.255
2020-02-05T21:27:43	David_McCann	i5	50000	5000000						3	0.255
2020-02-13T08:31:51	mnd9	office2	50000	5000000						3	0.255
2020-02-20T17:42:52	Keysarecool	i9	50000	5000000						3	0.255
2020-02-27T15:28:40	mnd9	75201b	50000	5000000						3	0.255
2020-03-05T05:21:42	MarkS	laptop64	50000	5000000						3	0.255
2020-03-11T21:15:58	mnd9	l2lounge	50000	5000000						3	0.255
2020-03-21T14:13:18	daveward2005	Davy	50000	5000000						3	0.255
2020-03-31T19:59:03	kracker	O0	50000	5000000						3	0.255
2020-04-13T14:02:13	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-04-24T10:30:54	nordi	sweet16	50000	5000000						3	0.255
2020-05-04T08:42:42	nordi	sweet16	50000	5000000						3	0.255
2020-05-13T13:33:31	nordi	sweet16	50000	5000000						3	0.255
2020-05-19T08:38:28	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-05-29T20:56:29	mnd9	libproj	50000	5000000						3	0.255
2020-06-17T12:18:40	mnd9	kitchen	50000	5000000						3	0.255
2020-06-29T18:28:25	GAN	LMS-12	50000	5000000						3	0.255
2020-07-07T05:59:40	mnd9	libproj	50000	5000000						3	0.255
2020-07-13T01:55:28	GAN	LMS-14	50000	5000000						3	0.255
2020-07-15T13:14:02	Ensigma	T470	50000	5000000						3	0.255
2020-07-25T07:28:32	GAN	LMS-02	50000	5000000	31840568463089992742234671	84.719	3	2	1176361261058116	3	0.255

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	A30C9774A3661DC1	0.137
2017-06-05T23:05:55	kkmrkkblmbrbk	c4.large	A30C9774A3661DC1	0.137

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 2246995, B2 = 8987980 (P-1 stage 2)

B1 = 2256995, B2 = 4513990 (P-1 stage 2)

B1 = 2246995, B2 = 4493990 (P-1 stage 2)

B1 = 2256995 (P-1 stage 1)

B1 = 2246995 (P-1 stage 1)

B1 = 2042723 (P-1 stage 1)

B1 = 1857021 (P-1 stage 1)

B1 = 1688201 (P-1 stage 1)

B1 = 1534729 (P-1 stage 1)

B1 = 1395209 (P-1 stage 1)

B1 = 1268372 (P-1 stage 1)

B1 = 1048242 (P-1 stage 1)

B1 = 866317 (P-1 stage 1)

B1 = 787561 (P-1 stage 1)

B1 = 715965 (P-1 stage 1)

B1 = 650878 (P-1 stage 1)

B1 = 591708 (P-1 stage 1)

B1 = 537917 (P-1 stage 1)

B1 = 444560 (P-1 stage 1)

B1 = 135000, B2 = 3071250 (P-1 stage 2)

B1 = 276039 (P-1 stage 1)

B1 = 250945 (P-1 stage 1)

B1 = 228132 (P-1 stage 1)

B1 = 207393 (P-1 stage 1)

B1 = 165915 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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