M1350779 Mersenne number exponent details

Residue

Status

L-L

8C9CFC300273ADA6

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	21.9976	68.6567%	500000	15000000	0.0714	4.8860%	22.0690	70.1882%	1.5314%
PrimeNet	2⁵⁶	0.0071	62.5000%	6000	100000	0.0006	2.6133%	0.0077	63.4800%	0.9800%
GPU72	2⁶⁰	0.1137	65.0000%	5500	40000	0.0004	0.9818%	0.1141	65.3436%	0.3436%
Difference	+7	+21.8839	+3.6567%	+494500	+14960000	+0.0710	+3.9042%	+21.9549	+4.8445%	+4.8445%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.9976

68.6567%

500000

15000000

0.0714

4.8860%

22.0690

70.1882%

1.5314%

PrimeNet

2⁵⁶

0.0071

62.5000%

6000

100000

0.0006

2.6133%

0.0077

63.4800%

0.9800%

GPU72

2⁶⁰

0.1137

65.0000%

5500

40000

0.0004

0.9818%

0.1141

65.3436%

0.3436%

Difference

+21.8839

+3.6567%

+494500

+14960000

+0.0710

+3.9042%

+21.9549

+4.8445%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1350779	2619995483053295937244154222207	31	101.047	969809081668169233177357 11 × 17041 × 394717 × 808559 × 16210669	2014-07-20	808559	16210669	1.004e+11	0.0912	0.0913

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1350779

2619995483053295937244154222207

101.047

969809081668169233177357
11 × 17041 × 394717 × 808559 × 16210669

2014-07-20

808559

16210669

1.004e+11

0.0912

0.0913

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.001	-	-	0.798%
2014-04-28T23:56:00	ANONYMOUS	Manual testing	175000	175000		-		-	-	0.010	-	-	1.156%
2014-07-20T00:27:00	mikr	MSI	500000	15000000			2619995483053295937244154222207	31	101.047	0.071	0.103	0.143	4.886%
2016-03-17T19:05:22	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.886%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.028	-	-
2022-03-07T17:32:36	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.085	-	-
2009-02-17T06:32:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.114	-	-
2011-05-09T14:43:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.227	-	-
2013-01-14T11:53:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.727	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.205 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:	25.205 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	11.74
250000	35000000		50	13.47

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-24T15:07:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-11-24T22:58:00	dachshund	Ann	50000	5000000						3	0.140
2009-04-28T23:55:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.140
2009-08-01T14:46:00	SubPrime	c2d0	50000	5000000						3	0.140
2009-11-22T07:49:00	SubPrime	c2d0	50000	5000000						3	0.140
2010-06-17T18:24:00	Charles A. Morris	pulsar	50000	5000000						3	0.140
2011-03-18T23:03:00	Beat Bucheli	I7	50000	5000000						3	0.140
2011-12-16T01:07:00	Oscar Östlin		50000	5000000						1	0.047
2012-06-18T09:59:00	soldake	athlonx3_435_unlock	50000	5000000						3	0.140
2012-12-05T13:06:00	OS1	Tina	50000	5000000						3	0.140
2013-10-14T13:52:00	jim f in mn	asus	50000	5000000						3	0.140
2014-03-02T01:32:00	Bruce	snowflake	50000	5000000						3	0.140
2014-04-02T05:14:00	Bruce	xps630	50000	5000000						3	0.140
2018-09-14T13:18:22	TJAOI	Manual testing	50000	5000000						216	10.10
2021-10-14T13:09:01	TJAOI	Manual testing	250000	35000000						50	13.47

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-05T00:00:00	JG12	v4_computers	8C9CFC300273ADA6	0.052
1998-08-09T00:00:00	JG12	v4_computers	8C9CFC300273ADA6	0.052
2010-02-25T04:36:00	Bruce A Metcalf	v4_computers	8C9CFC300273ADA6	0.052
2010-03-17T00:00:00	Bruce A Metcalf	v4_computers	8C9CFC300273ADA6	0.052

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 175000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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