M1818277 Mersenne number exponent details

Residue

Status

L-L

4A2A0188AD02C21E

double-checked

PRP

E3821312B467BB31

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	32.7810	69.1176%	1818277	181827700	0.9145	7.9916%	33.6955	71.5856%	2.4680%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8756%	0.0118	64.2173%	1.0594%
GPU72	2⁶¹	0.1689	65.5738%	9000	130000	0.0012	1.5576%	0.1702	66.1100%	0.5362%
Difference	+7	+32.6120	+3.5439%	+1809277	+181697700	+0.9133	+6.4340%	+33.5253	+5.4756%	+5.4756%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

32.7810

69.1176%

1818277

181827700

0.9145

7.9916%

33.6955

71.5856%

2.4680%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8756%

0.0118

64.2173%

1.0594%

GPU72

2⁶¹

0.1689

65.5738%

9000

130000

0.0012

1.5576%

0.1702

66.1100%

0.5362%

Difference

+32.6120

+3.5439%

+1809277

+181697700

+0.9133

+6.4340%

+33.5253

+5.4756%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1818277	667590744005738733842489	24	79.143	183577844301428972 2² × 45894461075357243	2020-11-10	4	45894461075357243	96,659	196,692,187	367,366,229
1818277	96847812708433245723214759	26	86.324	26631754322480360727 3 × 227 × 8839 × 4424350553353	2021-03-26	8839	4424350553353	14,042,022	18,962	35,415

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1818277

667590744005738733842489

79.143

183577844301428972
2² × 45894461075357243

2020-11-10

45894461075357243

96,659

196,692,187

367,366,229

1818277

96847812708433245723214759

86.324

26631754322480360727
3 × 227 × 8839 × 4424350553353

2021-03-26

8839

4424350553353

14,042,022

18,962

35,415

exponent	prime factors	composite factor	digits	bits*
1818277	667590744005738733842489 96847812708433245723214759	64654703341351389407056681159034834159665826095151	50	165.467

exponent

prime factors

composite factor

digits

bits*

1818277

667590744005738733842489
96847812708433245723214759

64654703341351389407056681159034834159665826095151

165.467

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-02-10T06:33:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.199%
2014-05-13T21:11:00	Jocelyn Larouche	Manual testing	135299	135299		-		-	-	0.011	-	-	0.924%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	170598	170598		-		-	-	0.013	-	-	1.050%
2015-05-28T00:39:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.485%
2018-09-10T11:51:56	Jocelyn Larouche	low 4M	1818277	181827700	12	-		-	-	0.915	-	-	7.992%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-02-10T06:33:00

Carsten Kossendey

leela

100000

1650000

0.015

-

-

2.199%

2014-05-13T21:11:00

Jocelyn Larouche

Manual testing

135299

0.011

-

-

0.924%

2014-09-22T21:00:00

Jocelyn Larouche

Manual testing

170598

0.013

-

-

1.050%

2015-05-28T00:39:00

mikr

MSI

2780000

91760000

0.600

-

-

7.485%

2018-09-10T11:51:56

Jocelyn Larouche

low 4M

1818277

181827700

0.915

-

-

7.992%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-17T14:28:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.169	-	-
2011-01-21T16:10:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.878	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.540	-	-
2015-04-24T21:33:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.080	-	-
2015-04-24T21:33:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.055	-	-
2015-09-02T13:37:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.110	-	-
2018-03-05T14:53:04	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.220	-	-
2019-06-17T12:15:00	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.44	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.930 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.930 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.250	0.026%
25	50000	0.746	47.415%
30	250000	0.046	95.502%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		176	12.15
50000	5000000	667590744005738733842489	6	0.414
50000	6600000		35	2.723
50000	6600000	96847812708433245723214759	34	2.645

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-22T14:22:00	Sturle Sunde	jobbtest	50000	5000000						3	0.207
2009-07-15T02:47:00	James Hintz	18_071409	50000	5000000						3	0.207
2010-10-28T11:00:00	Mistel		50000	5000000						3	0.207
2012-04-26T07:42:00	OS1	L3	50000	5000000						3	0.207
2013-08-05T12:12:00	OS1	L3	50000	5000000						3	0.207
2014-04-16T05:15:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-09-12T23:15:00	mikr	MSI	50000	5000000						12	0.828
2016-05-24T04:37:53	Bruce	DESK3	50000	5000000						3	0.207
2016-08-25T09:31:18	Bruce	DESK3	50000	5000000						3	0.207
2016-11-04T13:30:56	Bruce	DESK3	50000	5000000						3	0.207
2017-01-05T06:20:03	Bruce	DESK3	50000	5000000						3	0.207
2017-04-26T11:34:34	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-11-23T19:52:42	Bruce	DESK3	50000	5000000						3	0.207
2018-01-31T06:42:00	Bruce	DESK3	50000	5000000						3	0.207
2019-11-20T17:06:20	George Woltman	kaggle2	50000	5000000						3	0.207
2019-11-23T20:33:55	mnd9	dlounge	50000	5000000						3	0.207
2019-11-25T12:27:36	mnd9	50871	50000	5000000						3	0.207
2019-11-28T05:24:48	Alvin Bunk	i7-Core	50000	5000000						3	0.207
2019-12-02T13:12:56	mnd9	50871b	50000	5000000						3	0.207
2019-12-05T17:00:26	LordJulius	BlackboxNouveau	50000	5000000						3	0.207
2019-12-12T22:10:33	TheJudger	Sinope	50000	5000000						3	0.207
2019-12-14T21:04:38	Brett Walker	brain	50000	5000000						3	0.207
2019-12-19T20:44:15	Keysarecool	Boat_Anchor	50000	5000000						3	0.207
2019-12-26T18:19:34	MarkS	desktop-i7	50000	5000000						3	0.207
2019-12-31T09:53:52	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2020-01-05T22:42:46	cappy95833	HomePC	50000	5000000						3	0.207
2020-01-13T01:06:13	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2020-01-20T02:01:18	EricP	Cannonfodder	50000	5000000						3	0.207
2020-01-26T00:53:42	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2020-02-03T16:21:49	daveward2005	Davy	50000	5000000						3	0.207
2020-02-11T20:43:39	daveward2005	Davy	50000	5000000						3	0.207
2020-02-19T04:02:22	Brett Walker	brain	50000	5000000						3	0.207
2020-02-26T04:41:59	mnd9	75211backdoorb	50000	5000000						3	0.207
2020-03-04T06:02:42	mnd9	kitchen	50000	5000000						3	0.207
2020-03-10T08:37:17	MarkS	laptop64	50000	5000000						3	0.207
2020-03-18T09:01:03	mnd9	25836b	50000	5000000						3	0.207
2020-03-29T02:01:09	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2020-04-22T13:56:30	Keysarecool	Boat_Anchor	50000	5000000						3	0.207
2020-04-29T23:02:52	mnd9	fb	50000	5000000						3	0.207
2020-05-11T08:02:26	nordi	sweet16	50000	5000000						3	0.207
2020-06-08T01:16:58	ANONYMOUS	TimeVampireTheFifth	50000	5000000						3	0.207
2020-06-13T14:14:17	IanGlencross	glenx24	50000	5000000						3	0.207
2020-06-21T12:14:47	ANONYMOUS	TimeVampireTheFifth	50000	5000000						3	0.207
2020-06-28T05:40:45	debrouxl	8rd	50000	5000000						3	0.207
2020-07-05T08:32:45	daveward2005	Davy	50000	5000000						3	0.207
2020-07-12T04:42:10	GAN	AC-GR	50000	5000000						3	0.207
2020-07-18T05:48:04	Oliver Kruse	Krusen-NAS	50000	5000000						3	0.207
2020-07-24T10:30:57	GAN	KA-HP	50000	5000000						3	0.207
2020-08-01T09:14:11	debrouxl	8rd	50000	5000000						3	0.207
2020-08-07T23:11:56	mnd9	25836b	50000	5000000						3	0.207
2020-08-15T21:42:01	GAN	LMS-12	50000	5000000						3	0.207
2020-09-11T11:01:45	LordJulius	BlackboxNouveau	50000	5000000						7	0.483
2020-10-12T09:34:25	tottenhoff	4-of-4-Ryzen-5-3600	50000	5000000						7	0.483
2020-11-10T09:26:35	GAN	XPS	50000	5000000	667590744005738733842489	79.143	6	2	8199421464450955	6	0.414
2021-03-26T16:49:53	TJAOI	Manual testing	50000	6600000	96847812708433245723214759	86.324	34	2		34	2.645
2021-04-02T11:39:05	TJAOI	Manual testing	50000	6600000						35	2.723

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	4A2A0188AD02C21E	0.099
2015-07-01T17:35:00	MadPoo	Manual testing	4A2A0188AD02C21E	0.099

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

4A2A0188AD02C21E

0.099

2015-07-01T17:35:00

MadPoo

Manual testing

4A2A0188AD02C21E

0.099

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