M1274227 Mersenne number exponent details

Residue

Status

L-L

158C74695F36A6CD

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	23.3192	68.6567%	1195000	34655000	0.1387	6.2058%	23.4579	70.6018%	1.9451%
PrimeNet	2⁵⁶	0.0075	62.5000%	5500	90000	0.0005	2.4459%	0.0080	63.4172%	0.9172%
GPU72	2⁶⁰	0.1205	65.0000%	5500	36000	0.0003	0.9307%	0.1209	65.3257%	0.3257%
Difference	+7	+23.1986	+3.6567%	+1189500	+34619000	+0.1384	+5.2752%	+23.3370	+5.2761%	+5.2761%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.3192

68.6567%

1195000

34655000

0.1387

6.2058%

23.4579

70.6018%

1.9451%

PrimeNet

2⁵⁶

0.0075

62.5000%

5500

90000

0.0005

2.4459%

0.0080

63.4172%

0.9172%

GPU72

2⁶⁰

0.1205

65.0000%

5500

36000

0.0003

0.9307%

0.1209

65.3257%

0.3257%

Difference

+23.1986

+3.6567%

+1189500

+34619000

+0.1384

+5.2752%

+23.3370

+5.2761%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1274227	387262801557375903702463	24	78.358	151959894727303653 3 × 47 × 1283 × 840007599251	2013-10-29	1283	840007599251	95,180	2,103.3	3,928.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1274227

387262801557375903702463

78.358

151959894727303653
3 × 47 × 1283 × 840007599251

2013-10-29

1283

840007599251

95,180

2,103.3

3,928.3

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.240%
2013-10-07T16:33:00	David Campeau	i5-2500k	1195000	34655000		-		-	-	0.139	-	-	6.206%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-02-24T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.240%

2013-10-07T16:33:00

David Campeau

i5-2500k

1195000

34655000

0.139

-

-

6.206%

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		-	-	0.015	-	-
2003-06-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2022-03-07T17:32:05	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.090	-	-
2009-02-15T03:33:00	Sturle Sunde	buxtehude.ifi	2⁶⁰	2⁶¹		-	-	0.121	-	-
2012-09-15T18:40:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.241	-	-
2012-10-18T21:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.770	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.153 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	19.153 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.084	0.000%
25	50000	1.587	20.458%
30	250000	0.133	87.509%
35	1000000	0.009	99.085%

ECM Summary

B1	B2	factor	curves	GHz-days
		387262801557375903702463	1	0.00000e+0
50000	5000000		248	9.54
250000	25000000		50	9.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-11T17:42:00	James Heinrich	WHS	50000	5000000						1	0.038
2008-08-29T23:20:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-02-09T00:33:00	linded	kctz73a	50000	5000000						3	0.115
2009-07-09T21:35:00	Geoff Wing	GW1	50000	5000000						3	0.115
2009-10-20T14:42:00	SubPrime	c2d0	50000	5000000						3	0.115
2010-04-04T04:50:00	James Hintz	jeff4	50000	5000000						3	0.115
2011-01-07T10:16:00	eteo	stephanie	50000	5000000						3	0.115
2011-10-24T03:26:00	Andriy Makukha	freehost	50000	5000000						3	0.115
2012-07-19T13:16:00	Lackó	Iroda_Eva	50000	5000000						3	0.115
2013-02-11T08:37:00	OS1	Tina	50000	5000000						3	0.115
2013-10-29T17:05:00	jim f in mn	asus			387262801557375903702463	78.358		1		1	-
2017-12-15T15:35:07	TJAOI	Manual testing	50000	5000000						220	8.461
2021-01-29T12:53:10	TJAOI	Manual testing	250000	25000000						50	9.62

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 = 1195000, B2 = 34655000 (P-1 stage 2)

B1 = 1195000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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