M1372207 Mersenne number exponent details

Residue

Status

L-L

B301EFE27B6E6CF1

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	21.6541	68.6567%	500000	15000000	0.0714	4.8953%	21.7255	70.1911%	1.5344%
PrimeNet	2⁵⁶	0.0070	62.5000%	6000	100000	0.0006	2.6215%	0.0076	63.4831%	0.9831%
GPU72	2⁶⁰	0.1119	65.0000%	5500	60000	0.0005	1.1383%	0.1124	65.3984%	0.3984%
Difference	+7	+21.5422	+3.6567%	+494500	+14940000	+0.0709	+3.7570%	+21.6131	+4.7927%	+4.7927%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.6541

68.6567%

500000

15000000

0.0714

4.8953%

21.7255

70.1911%

1.5344%

PrimeNet

2⁵⁶

0.0070

62.5000%

6000

100000

0.0006

2.6215%

0.0076

63.4831%

0.9831%

GPU72

2⁶⁰

0.1119

65.0000%

5500

60000

0.0005

1.1383%

0.1124

65.3984%

0.3984%

Difference

+21.5422

+3.6567%

+494500

+14940000

+0.0709

+3.7570%

+21.6131

+4.7927%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1372207	639778072443173873975569	24	79.082	233120102303505912 2³ × 3 × 11 × 10487 × 124753 × 674953	2014-02-18	124753	674953	130,012	0.0086	0.0141

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1372207

639778072443173873975569

79.082

233120102303505912
2³ × 3 × 11 × 10487 × 124753 × 674953

2014-02-18

124753

674953

130,012

0.0086

0.0141

	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	228750		-		-	-	0.001	-	-	0.813%
unknown			500000	15000000		-	MISSED FACTOR!	-	-	0.071	-	-	4.895%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-21T00:00:00

ANONYMOUS

v4_computers

15000

228750

0.001

-

-

0.813%

unknown

500000

15000000

MISSED FACTOR!

0.071

-

-

4.895%

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	-	-
2022-03-07T17:32:38	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.084	-	-
2009-02-15T19:18:00	Sturle Sunde	herrick.ifi	2⁶⁰	2⁶¹		-	-	0.112	-	-
2012-08-10T08:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.224	-	-
2013-01-23T08:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.715	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.182 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	299 / 100	2.990	4.954%
25	50000	299 / 280	1.068	34.309%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.182 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.577	0.000%
25	50000	1.644	19.326%
30	250000	0.140	86.905%
35	1000000	0.010	99.023%

ECM Summary

B1	B2	factor	curves	GHz-days
		639778072443173873975569	1	0.00000e+0
50000	5000000		249	11.68
250000	35000000		50	13.51

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-28T19:26:00	James Heinrich	WHS	50000	5000000						1	0.047
2008-11-28T04:03:00	Architects Cubed	m1_19	50000	5000000						3	0.141
2009-05-09T07:29:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.141
2009-08-09T01:35:00	Geoff Wing	GW1	50000	5000000						3	0.141
2009-12-04T22:38:00	Lupo	yorick	50000	5000000						3	0.141
2010-07-07T04:42:00	Geoff Wing	GW1	50000	5000000						3	0.141
2011-04-04T17:45:00	greensinoz	giopa01	50000	5000000						3	0.141
2012-02-15T14:23:00	Bruce	GTLT-4540GZ	50000	5000000						3	0.141
2012-10-11T14:17:00	soldake		50000	5000000						3	0.141
2013-08-22T09:23:00	OS1	Tina	50000	5000000						3	0.141
2014-02-18T20:25:00	jim f in mn	asus			639778072443173873975569	79.082		1		1	-
2018-11-16T12:24:22	TJAOI	Manual testing	50000	5000000						221	10.36
2021-08-06T10:57:35	TJAOI	Manual testing	250000	35000000						50	13.51

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 = 228750 (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