M1330867 Mersenne number exponent details

Residue

Status

L-L

74D855AF2D45ED5C

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	2⁷⁰	179.5451	70.0000%	500000	15000000	0.0714	3.6255%	179.6165	71.0876%	1.0876%
PrimeNet	2⁵⁶	0.0072	62.5000%	6000	100000	0.0006	2.6056%	0.0078	63.4771%	0.9771%
GPU72	2⁶⁰	0.1154	65.0000%	5500	40000	0.0004	0.9784%	0.1158	65.3425%	0.3425%
Difference	+10	+179.4297	+5.0000%	+494500	+14960000	+0.0710	+2.6471%	+179.5007	+5.7452%	+5.7452%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

179.5451

70.0000%

500000

15000000

0.0714

3.6255%

179.6165

71.0876%

1.0876%

PrimeNet

2⁵⁶

0.0072

62.5000%

6000

100000

0.0006

2.6056%

0.0078

63.4771%

0.9771%

GPU72

2⁶⁰

0.1154

65.0000%

5500

40000

0.0004

0.9784%

0.1158

65.3425%

0.3425%

Difference

+10

+179.4297

+5.0000%

+494500

+14960000

+0.0710

+2.6471%

+179.5007

+5.7452%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1330867	18596874426496432093063	23	73.977	6986751653807793 3³ × 7² × 31 × 37 × 103 × 44700751	2014-02-18	103	44700751	2,306.3	0.1348	0.2518

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1330867

18596874426496432093063

73.977

6986751653807793
3³ × 7² × 31 × 37 × 103 × 44700751

2014-02-18

103

44700751

2,306.3

0.1348

0.2518

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-09-21T00:00:00	ANONYMOUS	v4_computers	15000	213750		-		-	-	0.001	-	-	0.489%
2016-03-17T19:05:05	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	3.625%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-21T00:00:00

ANONYMOUS

v4_computers

15000

213750

0.001

-

-

0.489%

2016-03-17T19:05:05

alpertron

Manual testing

500000

15000000

0.071

-

-

3.625%

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	-	-
2003-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.029	-	-
2022-03-07T17:32:34	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.087	-	-
2009-02-15T23:37:00	Sturle Sunde	scarpia.ifi	2⁶⁰	2⁶¹		-	-	0.115	-	-
2012-09-01T08:44:00	lycorn	Manual testing	2⁶¹	2⁶⁴		-	-	2.444	-	-
2013-10-19T11:56:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	2.807	-	-
2014-02-04T13:10:00	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	5.615	-	-
2014-02-04T13:10:00	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	11.23	-	-
2014-02-04T13:10:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	22.46	-	-
2014-02-04T13:10:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	44.92	-	-
2014-02-04T13:10:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	89.84	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.093 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	300 / 100	3.000	4.904%
25	50000	300 / 280	1.071	34.186%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.093 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.615	0.000%
25	50000	1.647	19.258%
30	250000	0.141	86.886%
35	1000000	0.010	99.022%

ECM Summary

B1	B2	factor	curves	GHz-days
		18596874426496432093063	1	0.00000e+0
50000	5000000		250	11.66
250000	35000000		50	13.43

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-19T13:04:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-09-10T14:44:00	Sturle Sunde	v23	50000	5000000						3	0.140
2009-02-21T00:54:00	Sturle Sunde	v21	50000	5000000						3	0.140
2009-07-25T14:48:00	Lupo	yorick	50000	5000000						3	0.140
2009-11-09T03:24:00	James Hintz	19_101609	50000	5000000						3	0.140
2010-06-12T04:57:00	Charles A. Morris	pulsar	50000	5000000						3	0.140
2011-02-24T23:41:00	Beat Bucheli	I7	50000	5000000						3	0.140
2011-11-20T13:09:00	Oscar Östlin		50000	5000000						1	0.047
2012-04-24T21:31:00	Lukasz Wrobel	4_core_L	50000	5000000						3	0.140
2012-11-07T03:16:00	ANONYMOUS		50000	5000000						3	0.140
2013-09-02T18:42:00	OS1	Tina	50000	5000000						3	0.140
2014-02-18T21:57:00	jim f in mn	asus			18596874426496432093063	73.977		1		1	-
2018-10-12T13:40:57	TJAOI	Manual testing	50000	5000000						221	10.31
2021-08-13T08:30:16	TJAOI	Manual testing	250000	35000000						50	13.43

date	userid	compid	res64	spent (GHz-days)
2010-03-17T00:00:00	Bruce A Metcalf	v4_computers	74D855AF2D45ED5C	0.051

date

userid

compid

res64

spent (GHz-days)

2010-03-17T00:00:00

Bruce A Metcalf

v4_computers

74D855AF2D45ED5C

0.051

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 = 15000, B2 = 213750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

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