M2427137 Mersenne number exponent details

Residue

Status

L-L

C3BCC9E3A9ED0770

double-checked

PRP

D40412EE55422228

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	2⁶⁹	49.1883	68.1159%	1986400	69524000	0.5550	6.5876%	49.7433	70.2163%	2.1004%
PrimeNet	2⁵⁹	0.0316	62.7119%	10000	180000	0.0019	2.5238%	0.0335	63.6529%	0.9411%
GPU72	2⁶³	0.6576	65.0794%	10000	150000	0.0017	1.3051%	0.6593	65.5351%	0.4557%
Difference	+6	+48.5307	+3.0366%	+1976400	+69374000	+0.5533	+5.2825%	+49.0840	+4.6812%	+4.6812%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

49.1883

68.1159%

1986400

69524000

0.5550

6.5876%

49.7433

70.2163%

2.1004%

PrimeNet

2⁵⁹

0.0316

62.7119%

10000

180000

0.0019

2.5238%

0.0335

63.6529%

0.9411%

GPU72

2⁶³

0.6576

65.0794%

10000

150000

0.0017

1.3051%

0.6593

65.5351%

0.4557%

Difference

+48.5307

+3.0366%

+1976400

+69374000

+0.5533

+5.2825%

+49.0840

+4.6812%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2427137	72118484021262018706732441	26	85.899	14856698245970874060 2² × 3² × 5 × 41 × 811 × 6841 × 362848637	2021-09-20	6841	362848637	5,702,085	1.9371	3.6168

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2427137

72118484021262018706732441

85.899

14856698245970874060
2² × 3² × 5 × 41 × 811 × 6841 × 362848637

2021-09-20

6841

362848637

5,702,085

1.9371

3.6168

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.188%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.169%
2010-11-17T11:34:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.219%
2010-12-17T22:28:00	markr	tiny	95000	1923750		-		-	-	0.019	-	-	2.094%
2014-04-26T06:21:00	mikr	MSI	1986400	69524000		-		-	-	0.555	-	-	6.588%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-10-08T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.188%

2010-11-10T11:27:00

Jocelyn Larouche

Manual testing

15000

0.001

-

-

0.169%

2010-11-17T11:34:00

Jocelyn Larouche

Manual testing

20000

0.002

-

-

0.219%

2010-12-17T22:28:00

markr

tiny

95000

1923750

0.019

-

-

2.094%

2014-04-26T06:21:00

mikr

MSI

1986400

69524000

0.555

-

-

6.588%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-14T20:44:00	Sturle Sunde	gimba.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-05T09:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.127	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.404	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.809	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.539	-	-
2015-10-23T09:34:51	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.079	-	-
2017-07-05T06:34:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.158	-	-
2019-04-22T13:11:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.32	-	-
2021-08-02T10:51:14	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	24.63	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.560 GHz-days
Estimated T-Level:	22.714

Digits	B1	Curves	Complete	FacMiss
20	11000	152 / 100	1.520	21.704%
25	50000	152 / 280	0.543	58.052%

New Calculation Method

Total ECM effort:	13.560 GHz-days
Estimated T-Level:	22.714

Digits	B1	Complete	FacMiss
20	11000	4.911	0.737%
25	50000	0.443	64.193%
30	250000	0.027	97.307%
35	1000000	0.001	99.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		138	12.30
50000	5000000	72118484021262018706732441	7	0.624
50000	5150000		7	0.632

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-17T09:24:00	Aca Arsov	backo6400	50000	5000000						3	0.267
2010-03-03T12:57:00	SubPrime	abd0	50000	5000000						3	0.267
2012-05-22T20:02:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.267
2013-12-14T06:50:00	arnaud	srv-630	50000	5000000						3	0.267
2015-07-03T10:10:00	guru	w1	50000	5000000						3	0.267
2016-02-20T09:51:14	Sintax	cloud2	50000	5000000						3	0.267
2016-06-09T09:09:46	Jason U	Server7	50000	5000000						3	0.267
2016-10-09T10:27:25	Bruce	Desk6	50000	5000000						3	0.267
2017-04-18T11:41:51	Bruce	Desk6	50000	5000000						3	0.267
2017-11-19T06:24:02	Bruce	Desk6	50000	5000000						3	0.267
2018-04-26T03:44:29	Bruce	Desk6	50000	5000000						3	0.267
2019-04-04T23:06:00	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.267
2020-04-21T02:18:24	mnd9	l2lounge	50000	5000000						3	0.267
2020-04-28T17:33:34	Keysarecool	Boat_Anchor	50000	5000000						3	0.267
2020-05-08T23:09:38	EricP	Cannonfodder	50000	5000000						3	0.267
2020-05-23T08:09:25	mnd9	libproj	50000	5000000						3	0.267
2020-06-11T09:02:41	GAN	KL-SCH04	50000	5000000						3	0.267
2020-06-26T20:26:32	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.267
2020-07-03T21:05:20	GAN	LMS-15	50000	5000000						3	0.267
2020-07-10T15:13:47	GAN	LMS-17	50000	5000000						3	0.267
2020-07-17T03:20:09	Nesowa	entropy_generator_2	50000	5000000						3	0.267
2020-07-22T20:16:47	daveward2005	Dave2	50000	5000000						3	0.267
2020-07-29T11:46:36	GAN	LMS-04	50000	5000000						3	0.267
2020-08-06T00:21:18	daveward2005	Dave2	50000	5000000						3	0.267
2020-08-14T16:17:19	mnd9	25836b	50000	5000000						3	0.267
2020-09-05T09:01:54	MarkS	desktop-i7	50000	5000000						7	0.624
2020-10-15T07:11:35	LaurV	bc1	50000	5000000						7	0.624
2020-11-06T12:13:29	lycorn	colab_ES	50000	5000000						7	0.624
2020-12-10T09:17:34	lycorn	colab_ES_1	50000	5000000						7	0.624
2021-02-11T05:47:48	LordJulius	Babybox	50000	5000000						7	0.624
2021-03-13T11:55:45	mnd9	75204b	50000	5000000						7	0.624
2021-03-14T02:00:05	mnd9	27016b	50000	5000000						7	0.624
2021-03-29T21:36:25	mnd9	75211frontb	50000	5000000						7	0.624
2021-06-09T23:43:51	kutens	vega	50000	5150000						7	0.632
2021-09-14T05:06:15	daveward2005	d12436	50000	5000000						7	0.624
2021-09-20T03:17:27	GAN	KL-SCH04	50000	5000000	72118484021262018706732441	85.899	7	2		7	0.624

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	C3BCC9E3A9ED0770	0.164
2018-05-21T09:27:07	kkmrkkblmbrbk	old	C3BCC9E3A9ED0770	0.164

date

userid

compid

res64

spent (GHz-days)

1999-04-02T00:00:00

ANONYMOUS

v4_computers

C3BCC9E3A9ED0770

0.164

2018-05-21T09:27:07

kkmrkkblmbrbk

old

C3BCC9E3A9ED0770

0.164

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