M1953587 Mersenne number exponent details

Residue

Status

L-L

1A1A8C16837E1E9E

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	30.5105	69.1176%	1953587	244198375	1.1919	8.4447%	31.7024	71.7256%	2.6079%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4676%	0.0208	64.6866%	0.8935%
GPU72	2⁶²	0.3145	66.1290%	8000	90000	0.0010	1.1536%	0.3155	66.5198%	0.3907%
Difference	+6	+30.1960	+2.9886%	+1945587	+244108375	+1.1909	+7.2912%	+31.3869	+5.2058%	+5.2058%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

30.5105

69.1176%

1953587

244198375

1.1919

8.4447%

31.7024

71.7256%

2.6079%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4676%

0.0208

64.6866%

0.8935%

GPU72

2⁶²

0.3145

66.1290%

8000

90000

0.0010

1.1536%

0.3155

66.5198%

0.3907%

Difference

+30.1960

+2.9886%

+1945587

+244108375

+1.1909

+7.2912%

+31.3869

+5.2058%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1953587	152826926468964625967605169	27	86.982	39114440889749119432 2³ × 3566687 × 1370825393767	2020-08-18	3566687	1370825393767	14,571,374	5,875.3	10,973

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1953587

152826926468964625967605169

86.982

39114440889749119432
2³ × 3566687 × 1370825393767

2020-08-18

3566687

1370825393767

14,571,374

5,875.3

10,973

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-05-16T18:46:00	kurly	hex	1000000	30000000		-		-	-	0.203	-	-	5.697%
2018-01-19T13:04:08	Jocelyn Larouche	low 4M	1953587	30000000	12	-		-	-	0.274	-	-	6.051%
2018-02-12T21:00:12	Jocelyn Larouche	low 4M	1953587	60000000	12	-		-	-	0.402	-	-	6.835%
2018-03-03T03:57:56	Jocelyn Larouche	low 4M	1953587	120000000	12	-		-	-	0.660	-	-	7.627%
2018-05-11T11:44:16	Jocelyn Larouche	low 4M	1953587	195358700	12	-		-	-	0.983	-	-	8.187%
2018-11-26T12:54:02	Jocelyn Larouche	Manual testing	1953587	244198375	12	-		-	-	1.192	-	-	8.445%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-05-16T18:46:00

kurly

hex

1000000

30000000

0.203

-

-

5.697%

2018-01-19T13:04:08

Jocelyn Larouche

low 4M

1953587

30000000

0.274

-

-

6.051%

2018-02-12T21:00:12

Jocelyn Larouche

low 4M

1953587

60000000

0.402

-

-

6.835%

2018-03-03T03:57:56

Jocelyn Larouche

low 4M

1953587

120000000

0.660

-

-

7.627%

2018-05-11T11:44:16

Jocelyn Larouche

low 4M

1953587

195358700

0.983

-

-

8.187%

2018-11-26T12:54:02

Jocelyn Larouche

Manual testing

1953587

244198375

1.192

-

-

8.445%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:29:00	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.059	-	-
2010-01-16T23:03:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.079	-	-
2016-02-23T16:29:00	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.157	-	-
2011-08-27T22:19:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.817	-	-
2016-02-23T16:29:00	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.502	-	-
2015-04-22T20:23:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.005	-	-
2015-04-22T20:23:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.913	-	-
2015-09-07T08:31:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.825	-	-
2018-02-05T16:30:32	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	7.650	-	-
2019-05-13T04:32:11	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.30	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.980 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:	18.980 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.470	0.021%
25	50000	0.759	46.828%
30	250000	0.047	95.420%
35	1000000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		138	9.60
50000	5000000	152826926468964625967605169	5	0.348
50000	7500000		108	9.029

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-16T04:36:00	Smurgs	Praca	50000	5000000						3	0.209
2009-08-16T08:01:00	SubPrime	stor	50000	5000000						3	0.209
2011-01-16T00:29:00	Lupo	yorick	50000	5000000						3	0.209
2012-11-25T12:09:00	Salvetay	server7	50000	5000000						3	0.209
2014-01-29T21:53:00	arnaud	srv-630	50000	5000000						3	0.209
2015-05-19T11:28:00	OS1	L3	50000	5000000						3	0.209
2016-02-10T15:54:52	James P McMillan	caturday	50000	5000000						3	0.209
2016-03-19T00:44:26	Jason U	Server7	50000	5000000						3	0.209
2016-07-01T16:33:31	StarionHost	Bluto	50000	5000000						3	0.209
2016-10-09T13:23:38	Bruce	Desk6	50000	5000000						3	0.209
2017-06-05T13:37:17	Bruce	Desk6	50000	5000000						3	0.209
2017-10-04T14:08:57	Bruce	Desk6	50000	5000000						3	0.209
2018-01-14T08:51:02	Bruce	Desk6	50000	5000000						3	0.209
2018-06-12T15:27:18	Bruce	Desk6	50000	5000000						3	0.209
2019-04-17T09:35:05	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.209
2019-12-06T07:21:48	Keysarecool	HPLaptop	50000	5000000						3	0.209
2019-12-10T20:41:26	J.R. Allen	lapacer	50000	5000000						3	0.209
2019-12-16T02:36:15	mnd9	50871b	50000	5000000						3	0.209
2019-12-21T15:38:06	mnd9	colab2	50000	5000000						3	0.209
2019-12-29T12:17:19	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.209
2020-01-01T05:47:23	Sergey Nosov	TS140-02	50000	5000000						3	0.209
2020-01-06T10:32:56	Yxinity	Olga	50000	5000000						3	0.209
2020-01-17T06:11:06	Palantsevich	OfficeB01	50000	5000000						3	0.209
2020-01-20T18:56:09	Bommer	3900X	50000	5000000						3	0.209
2020-01-27T09:18:43	mnd9	75204b	50000	5000000						3	0.209
2020-02-05T12:27:07	daveward2005	MW	50000	5000000						3	0.209
2020-02-12T18:56:54	EricP	Cannonfodder	50000	5000000						3	0.209
2020-02-19T23:25:43	EricP	Cannonfodder	50000	5000000						3	0.209
2020-02-27T06:12:51	mnd9	25836b	50000	5000000						3	0.209
2020-03-04T20:35:07	Keysarecool	HPLaptop	50000	5000000						3	0.209
2020-03-11T14:03:33	mnd9	office2	50000	5000000						3	0.209
2020-03-30T19:44:39	daveward2005	Davy	50000	5000000						3	0.209
2020-04-12T02:14:55	Keysarecool	HPLaptop	50000	5000000						3	0.209
2020-04-24T03:25:10	mnd9	libproj	50000	5000000						3	0.209
2020-05-01T00:13:30	mnd9	l2lounge	50000	5000000						3	0.209
2020-05-12T22:34:16	mnd9	27016b	50000	5000000						3	0.209
2020-05-18T17:42:01	mnd9	libproj	50000	5000000						3	0.209
2020-06-04T00:27:14	mnd9	50871b	50000	5000000						3	0.209
2020-06-16T00:55:15	Travis Glenn Russo	ROG-4900HS	50000	5000000						3	0.209
2020-06-29T17:18:45	mnd9	25836b	50000	5000000						3	0.209
2020-07-06T17:16:48	mnd9	libproj	50000	5000000						3	0.209
2020-07-12T15:56:34	GAN	LMS-03	50000	5000000						3	0.209
2020-07-18T18:04:37	GAN	LMS-14	50000	5000000						3	0.209
2020-07-24T19:34:42	GAN	OSB-02	50000	5000000						3	0.209
2020-07-31T22:11:39	GAN	LMS-08	50000	5000000						3	0.209
2020-08-08T16:24:27	GAN	LMS-18	50000	5000000						3	0.209
2020-08-18T13:41:12	mnd9	25836b	50000	5000000	152826926468964625967605169	86.982	5	2	2891347751518655	5	0.348
2022-05-12T09:18:05	TJAOI	Manual testing	50000	7500000						108	9.029

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	1A1A8C16837E1E9E	0.106
2015-07-10T01:00:00	MadPoo	Manual testing	1A1A8C16837E1E9E	0.106

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

ANONYMOUS

v4_computers

1A1A8C16837E1E9E

0.106

2015-07-10T01:00:00

MadPoo

Manual testing

1A1A8C16837E1E9E

0.106

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