M1363381 Mersenne number exponent details

Residue

Status

L-L

E771C7A4BF966985

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	2⁶⁷	21.7943	68.6567%	4258086	15000000	0.2681	5.7620%	22.0624	70.4627%	1.8060%
PrimeNet	2⁵⁶	0.0070	62.5000%	6000	100000	0.0006	2.6181%	0.0077	63.4818%	0.9818%
GPU72	2⁶⁰	0.1127	65.0000%	5500	50000	0.0004	1.0671%	0.1131	65.3735%	0.3735%
Difference	+7	+21.6816	+3.6567%	+4252586	+14950000	+0.2677	+4.6948%	+21.9493	+5.0892%	+5.0892%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.7943

68.6567%

4258086

15000000

0.2681

5.7620%

22.0624

70.4627%

1.8060%

PrimeNet

2⁵⁶

0.0070

62.5000%

6000

100000

0.0006

2.6181%

0.0077

63.4818%

0.9818%

GPU72

2⁶⁰

0.1127

65.0000%

5500

50000

0.0004

1.0671%

0.1131

65.3735%

0.3735%

Difference

+21.6816

+3.6567%

+4252586

+14950000

+0.2677

+4.6948%

+21.9493

+5.0892%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1363381	6632403854964530509497055244459641	34	112.353	2432336909112174259982006220 2² × 3 × 5 × 7 × 11 × 13 × 97 × 173 × 571 × 8839 × 266291 × 1795663	2014-08-21	266291	1795663	9.416e+10	0.0194	0.0300

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1363381

6632403854964530509497055244459641

112.353

2432336909112174259982006220
2² × 3 × 5 × 7 × 11 × 13 × 97 × 173 × 571 × 8839 × 266291 × 1795663

2014-08-21

266291

1795663

9.416e+10

0.0194

0.0300

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-07T00:00:00	Jocelyn Larouche	v4_computers	20000	280000		-		-	-	0.002	-	-	0.958%
2014-04-12T16:56:00	ANONYMOUS	Manual testing	150000	150000		-		-	-	0.008	-	-	1.066%
2014-04-20T11:29:00	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.011	-	-	1.241%
2014-08-21T08:37:00	mikr	MSI	4258086	15000000			6632403854964530509497055244459641	34	112.353	0.236	0.104	0.471	5.762%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.028	-	-
2022-03-07T17:32:37	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.084	-	-
2009-02-17T00:23:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.113	-	-
2011-05-09T14:44:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.225	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.720	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.246 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.246 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.76
250000	35000000		50	13.49

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-27T07:07:00	Steve Scott	Abit	50000	5000000						1	0.047
2009-02-18T16:20:00	oodaira	Win02	50000	5000000						3	0.141
2009-05-06T17:03:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.141
2009-08-07T16:58:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.141
2009-11-29T21:30:00	KayJongsma	Wolter1	50000	5000000						3	0.141
2010-06-29T17:18:00	Charles A. Morris	magnetar	50000	5000000						3	0.141
2011-03-26T18:13:00	OS1	Tina	50000	5000000						3	0.141
2012-01-23T09:21:00	Oscar Östlin		50000	5000000						1	0.047
2012-07-11T08:17:00	soldake		50000	5000000						3	0.141
2013-01-24T09:48:00	OS1	Tina	50000	5000000						3	0.141
2013-11-05T16:55:00	jim f in mn	asus	50000	5000000						3	0.141
2014-03-02T16:30:00	Bruce	snowflake	50000	5000000						3	0.141
2014-05-02T14:52:00	OS1	Tina	50000	5000000						3	0.141
2018-10-26T10:44:15	TJAOI	Manual testing	50000	5000000						216	10.12
2021-06-26T09:33:12	TJAOI	Manual testing	250000	35000000						50	13.49

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 = 4258086, B2 = 15000000 (P-1 stage 2)

B1 = 4258086 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 150000 (P-1 stage 1)

B1 = 20000, B2 = 280000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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