M2095081 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	28.4499	69.1176%	2500000	125000000	0.8746	7.8965%	29.3246	71.5563%	2.4386%
PrimeNet	2⁵⁸	0.0183	63.7931%	9000	160000	0.0016	2.6766%	0.0200	64.7622%	0.9691%
GPU72	2⁶²	0.2932	66.1290%	9000	140000	0.0015	1.4010%	0.2948	66.6036%	0.4745%
Difference	+6	+28.1567	+2.9886%	+2491000	+124860000	+0.8731	+6.4955%	+29.0298	+4.9527%	+4.9527%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2095081	1657578132391416280658087	25	80.455	395588078072259803 211 × 271 × 6918173485463	2020-08-18	271	6918173485463	205,496	35,935	67,116

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%
2009-07-27T06:36:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.876%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.351%
2011-01-09T14:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.510%
2011-01-22T09:53:00	James Heinrich	Q6600	140000	3150000		-		-	-	0.029	-	-	2.794%
2016-07-27T10:56:35	Jocelyn Larouche	Manual testing	186340	6300000	12	-		-	-	0.050	-	-	3.411%
2016-11-05T16:28:43	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.240%
2016-11-10T03:36:30	Jocelyn Larouche	low 4M	268329	268329		-		-	-	0.026	-	-	1.358%
2017-05-24T12:30:58	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.896%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-02T20:11:00	Sturle Sunde	nardi.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-23T22:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.147	-	-
2013-09-03T09:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.469	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.937	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.783	-	-
2015-11-02T09:33:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.567	-	-
2016-09-22T02:15:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.134	-	-
2019-04-01T03:15:25	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.27	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.038 GHz-days
Estimated T-Level:	22.107

Digits	B1	Curves	Complete	FacMiss
20	11000	118 / 100	1.180	30.546%
25	50000	118 / 280	0.421	65.561%

New Calculation Method

Total ECM effort:	10.038 GHz-days
Estimated T-Level:	22.107

Digits	B1	Complete	FacMiss
20	11000	4.538	1.069%
25	50000	0.420	65.709%
30	250000	0.026	97.386%
35	1000000	0.001	99.876%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		117	9.95
50000	5000000	1657578132391416280658087	1	0.085

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-10T04:11:00	Nathan Slaven	q6600	50000	5000000						3	0.255
2009-11-08T18:19:00	SubPrime	stor	50000	5000000						3	0.255
2011-06-09T10:23:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-27T19:41:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-09-30T23:42:00	arnaud	srv-630	50000	5000000						3	0.255
2015-07-29T15:50:00	guru	w1	50000	5000000						3	0.255
2016-04-23T17:59:05	lettp	Home	50000	5000000						3	0.255
2016-05-29T10:26:15	Logan MCI	L-LAPTOP	50000	5000000						3	0.255
2016-08-12T09:12:25	Bruce	test	50000	5000000						3	0.255
2017-01-23T12:25:19	Bruce	Desk6	50000	5000000						3	0.255
2017-08-13T22:51:35	Bruce	Desk6	50000	5000000						3	0.255
2017-12-30T00:24:42	alphaLONE	7ubuSTEC	50000	5000000						3	0.255
2018-06-09T15:25:05	Bruce	Desk6	50000	5000000						3	0.255
2019-02-27T07:04:13	zar	eng1	50000	5000000						3	0.255
2020-01-06T07:00:29	IanGlencross	glenx24	50000	5000000						3	0.255
2020-01-14T22:34:13	Nesowa	6700T	50000	5000000						3	0.255
2020-01-27T02:15:28	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-02-05T02:09:49	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-02-13T08:13:25	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-02-20T12:38:53	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-02-27T00:38:05	mnd9	75201b	50000	5000000						3	0.255
2020-03-04T13:45:12	mat10243x	K3	50000	5000000						3	0.255
2020-03-11T13:56:41	mnd9	kitchen	50000	5000000						3	0.255
2020-03-19T03:47:20	mnd9	75211backdoorb	50000	5000000						3	0.255
2020-03-21T15:48:10	kracker	O0	50000	5000000						3	0.255
2020-03-30T10:04:32	mnd9	221Rb	50000	5000000						3	0.255
2020-04-12T03:03:38	mnd9	libproj	50000	5000000						3	0.255
2020-04-23T09:53:44	EricP	Cannonfodder	50000	5000000						3	0.255
2020-05-01T04:37:12	mnd9	75211backdoorb	50000	5000000						3	0.255
2020-05-12T09:42:06	nordi	sweet16	50000	5000000						3	0.255
2020-05-28T09:44:55	Yxinity	Olga	50000	5000000						3	0.255
2020-06-15T16:21:51	lycorn	colab_ES	50000	5000000						3	0.255
2020-06-29T05:41:30	daveward2005	Davy	50000	5000000						3	0.255
2020-07-06T01:32:12	GAN	LMS-04	50000	5000000						3	0.255
2020-07-12T15:05:06	daveward2005	Dave2	50000	5000000						3	0.255
2020-07-18T10:34:45	MarkS	desktop-i7	50000	5000000						3	0.255
2020-07-24T15:25:58	GAN	OSB-02	50000	5000000						3	0.255
2020-08-08T10:28:43	-Anonymous-	aws	50000	5000000						3	0.255
2020-08-18T12:19:51	rextherunt	ice	50000	5000000	1657578132391416280658087	80.455	1	2		1	0.085
2020-08-27T00:33:33	mnd9	kitchen	50000	5000000						3	0.255

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	767EF3478036548D	0.138
2017-06-13T00:00:29	kkmrkkblmbrbk	c4.large	767EF3478036548D	0.138

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 186340, B2 = 6300000 (P-1 stage 2)

B1 = 140000, B2 = 3150000 (P-1 stage 2)

B1 = 268329 (P-1 stage 1)

B1 = 223608 (P-1 stage 1)

B1 = 186340 (P-1 stage 1)

B1 = 140000 (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

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