M2142967 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	27.8142	67.6471%	2500000	125000000	0.8746	7.9143%	28.6888	70.2076%	2.5605%
PrimeNet	2⁵⁸	0.0179	62.0690%	9000	170000	0.0017	2.7321%	0.0196	63.1053%	1.0363%
GPU72	2⁶²	0.2867	64.5161%	10000	150000	0.0017	1.4880%	0.2884	65.0441%	0.5280%
Difference	+6	+27.5275	+3.1309%	+2490000	+124850000	+0.8730	+6.4264%	+28.4005	+5.1635%	+5.1635%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2142967	5338251154029094211162753	25	82.143	1245528081867124928 2⁶ × 5581 × 3487076917967	2020-07-07	5581	3487076917967	505,339	18,113	33,830

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.225%
2010-11-02T22:12:00	ANONYMOUS	Manual testing	20000	20000		-		-	-	0.002	-	-	0.254%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.353%
2011-01-13T23:58:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.512%
2011-01-24T16:21:00	James Heinrich	i7-920	130000	2632500		-		-	-	0.025	-	-	2.654%
2014-10-28T23:25:00	Jocelyn Larouche	Manual testing	159951	159951		-		-	-	0.015	-	-	1.044%
2016-06-06T01:26:58	Jocelyn Larouche	Manual testing	175946	5265000	6	-		-	-	0.043	-	-	3.265%
2016-11-13T02:06:36	Jocelyn Larouche	low 4M	211135	211135		-		-	-	0.020	-	-	1.208%
2017-04-22T17:25:11	Jocelyn Larouche	low 4M	351892	3518920	6	-		-	-	0.050	-	-	3.301%
2017-04-27T04:20:45	Jocelyn Larouche	low 4M	422270	4222700	6	-		-	-	0.060	-	-	3.520%
2017-11-03T15:49:13	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.914%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T20:28:00	Sturle Sunde	foster.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2009-01-07T04:46:00	Sturle Sunde	ginjtje.ifi	2⁶¹	2⁶²		-	-	0.143	-	-
2013-09-07T11:35:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.458	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.916	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.744	-	-
2015-12-27T16:49:16	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.487	-	-
2016-10-29T15:24:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.974	-	-
2019-04-15T13:43:12	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.95	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.105 GHz-days
Estimated T-Level:	4.750

Digits	B1	Curves	Complete	FacMiss
20	11000	95 / 100	0.950	38.490%
25	50000	95 / 280	0.339	71.185%

New Calculation Method

Total ECM effort:	8.105 GHz-days
Estimated T-Level:	4.750

Digits	B1	Complete	FacMiss
20	11000	3.065	4.668%
25	50000	0.277	75.808%
30	250000	0.017	98.309%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		93	7.934
50000	5000000	5338251154029094211162753	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-08T06:14:00	mdrg	MDRG02	50000	5000000						3	0.256
2009-11-24T17:03:00	SubPrime	abd0	50000	5000000						3	0.256
2011-08-05T05:29:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-23T06:18:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.256
2015-01-03T21:40:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2015-10-29T06:22:05	lopper	i5-4670	50000	5000000						3	0.256
2015-12-18T09:55:39	guru	w6	50000	5000000						3	0.256
2016-06-15T15:50:35	Jason U	Server7	50000	5000000						3	0.256
2016-09-19T19:29:23	Bruce	Desk6	50000	5000000						3	0.256
2017-03-14T07:53:47	Bruce	Desk6	50000	5000000						3	0.256
2017-10-05T00:23:29	Bruce	Desk6	50000	5000000						3	0.256
2018-02-10T21:48:04	Bruce	Desk6	50000	5000000						3	0.256
2018-07-24T13:40:09	Bruce	Desk6	50000	5000000						3	0.256
2019-10-10T19:52:25	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-22T08:14:04	David_McCann	i5	50000	5000000						3	0.256
2020-01-29T13:18:59	mat10243x	C2	50000	5000000						3	0.256
2020-02-07T16:44:00	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.256
2020-02-14T17:09:59	Alvin Bunk	BADCAT	50000	5000000						3	0.256
2020-02-22T03:49:47	daveward2005	Davy	50000	5000000						3	0.256
2020-02-28T18:59:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-03-06T11:36:20	kracker	O0	50000	5000000						3	0.256
2020-03-13T05:29:35	Nesowa	6700T	50000	5000000						3	0.256
2020-03-21T05:52:28	kracker	O0	50000	5000000						3	0.256
2020-04-02T10:18:11	Alvin Bunk	BADCAT	50000	5000000						3	0.256
2020-04-16T05:33:57	mnd9	libproj	50000	5000000						3	0.256
2020-04-25T14:35:14	nordi	sweet16	50000	5000000						3	0.256
2020-05-06T13:04:50	SXS2297	M-Laptop	50000	5000000						3	0.256
2020-05-14T23:13:07	MarkS	desktop-i7	50000	5000000						3	0.256
2020-06-01T12:12:17	mnd9	kitchen	50000	5000000						3	0.256
2020-06-21T08:39:54	IanGlencross	glenx24	50000	5000000						3	0.256
2020-06-30T22:29:32	GAN	LMS-16	50000	5000000						3	0.256
2020-07-07T20:57:24	GAN	OSK-SEK	50000	5000000	5338251154029094211162753	82.143	2	2	6268551650473696	2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	71DFFCA3BDDD7E7C	0.141
2018-04-07T20:21:29	kkmrkkblmbrbk	old	71DFFCA3BDDD7E7C	0.141

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 = 422270, B2 = 4222700 (P-1 stage 2)

B1 = 351892, B2 = 3518920 (P-1 stage 2)

B1 = 175946, B2 = 5265000 (P-1 stage 2)

B1 = 422270 (P-1 stage 1)

B1 = 351892 (P-1 stage 1)

B1 = 130000, B2 = 2632500 (P-1 stage 2)

B1 = 211135 (P-1 stage 1)

B1 = 175946 (P-1 stage 1)

B1 = 159951 (P-1 stage 1)

B1 = 130000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

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)

10²

10³

10⁴

10⁵

10⁶

10⁷

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