M2138713 Mersenne number exponent details

Residue

Status

L-L

3163E794A40D6ABD

double-checked

PRP

67045514287E4DCC

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	27.8695	67.6471%	2500000	125000000	0.8746	7.9127%	28.7441	70.2071%	2.5600%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7310%	0.0196	63.1049%	1.0359%
GPU72	2⁶²	0.2873	64.5161%	10000	150000	0.0017	1.4874%	0.2889	65.0439%	0.5278%
Difference	+6	+27.5822	+3.1309%	+2490000	+124850000	+0.8730	+6.4254%	+28.4552	+5.1632%	+5.1632%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

27.8695

67.6471%

2500000

125000000

0.8746

7.9127%

28.7441

70.2071%

2.5600%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

170000

0.0017

2.7310%

0.0196

63.1049%

1.0359%

GPU72

2⁶²

0.2873

64.5161%

10000

150000

0.0017

1.4874%

0.2889

65.0439%

0.5278%

Difference

+27.5822

+3.1309%

+2490000

+124850000

+0.8730

+6.4254%

+28.4552

+5.1632%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2138713	634920769672256881145929	24	79.071	148435243455353028 2² × 3 × 137 × 90289077527587	2021-05-01	137	90289077527587	99,475	468,984	875,932

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2138713

634920769672256881145929

79.071

148435243455353028
2² × 3 × 137 × 90289077527587

2021-05-01

137

90289077527587

99,475

468,984

875,932

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.225%
2010-10-26T07:05:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.669%
2010-11-27T11:57:00	Oscar Östlin		80000	1500000		-		-	-	0.015	-	-	2.103%
2013-12-03T16:49:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.097	-	-	4.330%
2017-10-20T05:13:41	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.913%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-03-07T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.225%

2010-10-26T07:05:00

Oscar Östlin

75011

0.007

-

-

0.669%

2010-11-27T11:57:00

Oscar Östlin

80000

1500000

0.015

-

-

2.103%

2013-12-03T16:49:00

c10ck3r

Manual testing

500000

10000000

0.097

-

-

4.330%

2017-10-20T05:13:41

mikr

MSI

2500000

125000000

0.875

-

-

7.913%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:06	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T23:49:00	Sturle Sunde	figaro.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-16T06:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.459	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.918	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.747	-	-
2015-12-27T16:49:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.494	-	-
2016-10-29T15:24:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.988	-	-
2019-04-22T13:11:42	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.98	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.235 GHz-days
Estimated T-Level:	22.929

Digits	B1	Curves	Complete	FacMiss
20	11000	164 / 100	1.640	19.239%
25	50000	164 / 280	0.586	55.612%

New Calculation Method

Total ECM effort:	14.235 GHz-days
Estimated T-Level:	22.929

Digits	B1	Complete	FacMiss
20	11000	5.329	0.485%
25	50000	0.483	61.687%
30	250000	0.030	97.060%
35	1000000	0.001	99.863%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		153	13.05
50000	5000000	634920769672256881145929	3	0.256
50000	6750000		7	0.683
76620	24176890		1	0.246

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-02T14:25:00	dragon325	x-liberty	50000	5000000						3	0.256
2009-11-24T08:40:00	SubPrime	stor	50000	5000000						3	0.256
2011-07-30T14:21:00	Andrew B	dell_xps_8100_i7_x86	50000	5000000						3	0.256
2013-04-21T09:30:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.256
2014-12-17T16:30:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2015-08-13T22:16:00	guru	w6	50000	5000000						3	0.256
2016-03-14T04:00:50	Dave Matthews	VMW7-001	50000	5000000						3	0.256
2016-06-13T17:32:42	Bruce	Desk6	50000	5000000						3	0.256
2016-09-15T18:55:25	Bruce	Desk6	50000	5000000						3	0.256
2017-03-11T03:22:19	Bruce	Desk6	50000	5000000						3	0.256
2017-09-25T04:20:17	Bruce	Desk6	50000	5000000						3	0.256
2018-02-06T21:18:48	Bruce	Desk6	50000	5000000						3	0.256
2018-07-21T01:54:01	Bruce	Desk6	50000	5000000						3	0.256
2019-10-04T12:46:47	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-20T21:46:09	EricP	Cannonfodder	50000	5000000						3	0.256
2020-01-27T08:17:12	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-02-05T13:45:05	David_McCann	i5	50000	5000000						3	0.256
2020-02-13T03:04:32	daveward2005	Davy	50000	5000000						3	0.256
2020-02-20T09:40:16	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-02-27T00:47:38	Nesowa	entropy_generator_2	50000	5000000						3	0.256
2020-03-04T23:12:46	mnd9	50869b	50000	5000000						3	0.256
2020-03-11T18:59:41	mnd9	office2	50000	5000000						3	0.256
2020-03-19T04:31:30	mnd9	l2lounge	50000	5000000						3	0.256
2020-03-31T10:17:29	Alvin Bunk	BADCAT	50000	5000000						3	0.256
2020-04-13T01:37:05	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-04-24T08:32:37	mnd9	libproj	50000	5000000						3	0.256
2020-05-01T13:28:30	nordi	sweet16	50000	5000000						3	0.256
2020-05-13T11:16:46	Akmal Sultonov	B830	50000	5000000						3	0.256
2020-05-13T14:20:01	Akmal Sultonov	B830	50000	5000000						3	0.256
2020-05-15T03:07:40	Massimo Cappelli (ik5pwa)	maxwinxp_1	50000	5000000						3	0.256
2020-06-29T17:41:51	MarkS	desktop-i7	50000	5000000						3	0.256
2020-07-06T23:30:20	mnd9	25836b	50000	5000000						3	0.256
2020-07-12T20:28:50	GAN	LMS-18	50000	5000000						3	0.256
2020-07-18T20:16:06	GAN	LMS-14	50000	5000000						3	0.256
2020-07-25T09:35:46	rextherunt	ice	50000	5000000						3	0.256
2020-08-01T09:25:48	lycorn	colab_S	50000	5000000						3	0.256
2020-08-08T21:45:59	GAN	LMS-15	50000	5000000						3	0.256
2020-08-22T12:52:29	Leo Custodio	GCP-013	50000	5000000						7	0.597
2020-09-23T21:41:37	Nesowa	6700T	50000	5000000						7	0.597
2020-10-21T02:33:06	Albrecht Heeffer	Ryzen52	50000	5000000						7	0.597
2020-11-09T21:38:48	Bruno Victal	Manual testing	76620	24176890						1	0.246
2020-12-12T09:28:15	Zenzoma	AMD3970X	50000	5000000						7	0.597
2021-01-13T15:00:52	lycorn	colab_A_1	50000	6750000						7	0.683
2021-02-17T03:48:39	MarkS	desktop-i7	50000	5000000						7	0.597
2021-03-18T00:57:09	mnd9	75204	50000	5000000						7	0.597
2021-05-01T05:19:21	GAN	KL-SCH07	50000	5000000	634920769672256881145929	79.071	3	2	606656774781261	3	0.256

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	3163E794A40D6ABD	0.141
1999-04-13T00:00:00	ANONYMOUS	v4_computers	3163E794A40D6ABD	0.141
2018-04-07T06:20:21	kkmrkkblmbrbk	old	3163E794A40D6ABD	0.141

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

3163E794A40D6ABD

0.141

1999-04-13T00:00:00

ANONYMOUS

v4_computers

3163E794A40D6ABD

0.141

2018-04-07T06:20:21

kkmrkkblmbrbk

old

3163E794A40D6ABD

0.141

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