M2114977 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	28.1823	67.6471%	2500000	125000000	0.8746	7.9039%	29.0569	70.2042%	2.5572%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6813%	0.0198	63.0860%	1.0171%
GPU72	2⁶²	0.2905	64.5161%	10000	140000	0.0016	1.4534%	0.2921	65.0319%	0.5157%
Difference	+6	+27.8918	+3.1309%	+2490000	+124860000	+0.8730	+6.4505%	+28.7648	+5.1724%	+5.1724%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2114977	153714765888080126813811547583	30	96.956	36339583335440557229183 7 × 5191369047920079604169	2020-07-06	7	5191369047920079604169	7.921e+9	2.697e+13	5.036e+13

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	-	-	0.224%
2009-08-02T13:04:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.878%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.352%
2011-01-10T23:58:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.511%
2011-01-28T08:57:00	James Heinrich	i7-920	140000	3010000		-		-	-	0.028	-	-	2.769%
2016-07-23T03:38:16	Jocelyn Larouche	Manual testing	186340	6020000	12	-		-	-	0.048	-	-	3.384%
2016-11-10T03:36:30	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.242%
2017-06-10T03:57:36	Jocelyn Larouche	low 4M	372680	3726800	6	-		-	-	0.053	-	-	3.363%
2017-06-28T04:14:46	Jocelyn Larouche	low 4M	447216	4472160	6	-		-	-	0.064	-	-	3.585%
2017-08-03T23:30:20	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.904%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T01:48:00	Sturle Sunde	giacco.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-04-01T20:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.145	-	-
2013-09-05T08:28:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.464	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.928	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.767	-	-
2015-12-27T16:49:20	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.533	-	-
2016-10-15T17:13:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.066	-	-
2019-05-13T13:38:20	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.13	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.262 GHz-days
Estimated T-Level:	4.850

Digits	B1	Curves	Complete	FacMiss
20	11000	97 / 100	0.970	37.724%
25	50000	97 / 280	0.346	70.677%

New Calculation Method

Total ECM effort:	8.262 GHz-days
Estimated T-Level:	4.850

Digits	B1	Complete	FacMiss
20	11000	3.129	4.376%
25	50000	0.283	75.367%
30	250000	0.017	98.274%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		96	8.177
50000	5000000	153714765888080126813811547583	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-13T15:05:00	Matthias Eckoldt	serverSP	50000	5000000						3	0.256
2009-11-18T04:44:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.256
2011-07-12T18:55:00	Csaba Vágó	timigep	50000	5000000						3	0.256
2013-04-11T22:05:00	jim f in mn	asus	50000	5000000						3	0.256
2014-11-09T13:54:00	dragon325	Falken-i7-920	50000	5000000						3	0.256
2015-08-05T07:18:00	guru	w1	50000	5000000						3	0.256
2016-02-23T01:16:35	Bruce	Desk6	50000	5000000						3	0.256
2016-05-31T21:37:16	lettp	Home	50000	5000000						3	0.256
2016-08-21T10:14:05	Bruce	test	50000	5000000						3	0.256
2017-02-19T18:55:09	Bruce	Desk6	50000	5000000						3	0.256
2017-09-04T11:49:53	Bruce	Desk6	50000	5000000						3	0.256
2018-01-18T16:11:39	Bruce	Desk6	50000	5000000						3	0.256
2018-06-29T17:50:37	Bruce	Desk6	50000	5000000						3	0.256
2019-07-06T05:08:47	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-13T23:19:47	Sergey Nosov	TS140-02	50000	5000000						3	0.256
2020-01-20T14:50:48	daveward2005	MW	50000	5000000						3	0.256
2020-01-26T11:16:08	IanGlencross	glenx24	50000	5000000						3	0.256
2020-02-04T06:06:02	IanGlencross	glenx24	50000	5000000						3	0.256
2020-02-12T13:01:35	mnd9	75201b	50000	5000000						3	0.256
2020-02-19T10:52:24	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-02-26T12:27:21	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-03-04T06:41:20	EricP	Cannonfodder	50000	5000000						3	0.256
2020-03-15T22:16:43	S04803	lfmcal	50000	5000000						3	0.256
2020-03-18T12:57:09	mnd9	f4b	50000	5000000						3	0.256
2020-03-29T23:19:13	nranks	wlaptop	50000	5000000						3	0.256
2020-04-11T08:34:10	mnd9	libproj	50000	5000000						3	0.256
2020-04-23T00:50:26	mnd9	fb	50000	5000000						3	0.256
2020-04-30T10:30:11	mnd9	eileen	50000	5000000						3	0.256
2020-05-12T15:48:46	mnd9	25836b	50000	5000000						3	0.256
2020-05-27T00:30:11	mnd9	office2	50000	5000000						3	0.256
2020-06-15T12:28:53	daveward2005	MW	50000	5000000						3	0.256
2020-06-28T17:38:37	GAN	GAN-HP	50000	5000000						3	0.256
2020-07-06T03:55:18	mnd9	libproj	50000	5000000	153714765888080126813811547583	96.956	1	2	900506774758078	1	0.085

date	userid	compid	res64	spent (GHz-days)
1997-11-29T00:00:00	ANONYMOUS	v4_computers	6C6C716CA59DD062	0.139
1999-07-30T00:00:00	ANONYMOUS	v4_computers	CEBC9AF174778F__	0.139
1999-09-07T00:00:00	ANONYMOUS	v4_computers	6C6C716CA59DD062	0.139

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 = 447216, B2 = 4472160 (P-1 stage 2)

B1 = 372680, B2 = 3726800 (P-1 stage 2)

B1 = 186340, B2 = 6020000 (P-1 stage 2)

B1 = 447216 (P-1 stage 1)

B1 = 372680 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

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