M3462947 Mersenne number exponent details

Residue

Status

L-L

6752CFB670B2A162

double-checked

PRP

36B7B781D866FE80

double-checked

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	34.4755	68.1159%	20000000	1000000000	11.1771	11.6152%	45.6525	79.7311%	16.3978%
PrimeNet	2⁶⁰	0.0444	63.3333%	15000	280000	0.0045	2.9033%	0.0488	66.2366%	2.9033%
GPU72	2⁶⁴	1.0278	65.6250%	19000	360000	0.0057	1.8851%	1.0336	67.5101%	1.8851%
Difference	+5	+33.4477	+2.4909%	+19981000	+999640000	+11.1713	+9.7301%	+44.6190	+12.2211%	+12.2211%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.4755

68.1159%

20000000

1000000000

11.1771

11.6152%

45.6525

79.7311%

16.3978%

PrimeNet

2⁶⁰

0.0444

63.3333%

15000

280000

0.0045

2.9033%

0.0488

66.2366%

2.9033%

GPU72

2⁶⁴

1.0278

65.6250%

19000

360000

0.0057

1.8851%

1.0336

67.5101%

1.8851%

Difference

+33.4477

+2.4909%

+19981000

+999640000

+11.1713

+9.7301%

+44.6190

+12.2211%

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
3462947	177322243499969706539110954183491697044649	42	137.025	25602794888280084352880791156129692 2² × 3 × 7 × 43 × 67 × 79 × 239 × 46567 × 219787 × 774119 × 707215633	774119	707215633	2021-02-26	4.482e+10	5.9794	10.960

GHz-days

exponent

factor

digits

bits*

min B1

min B2

date found

min. TF

min. P-1

normal P-1

3462947

177322243499969706539110954183491697044649

137.025

25602794888280084352880791156129692
2² × 3 × 7 × 43 × 67 × 79 × 239 × 46567 × 219787 × 774119 × 707215633

774119

707215633

2021-02-26

4.482e+10

5.9794

10.960

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:12:00	Carsten Kossendey	leela	20000	235000		-		-	-	0.005	-	-	0.806%
2011-11-08T13:25:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.687%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78535	78535		-		-	-	0.012	-	-	0.653%
2014-09-23T09:31:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.164%
2021-02-26T12:56:27	axn	Manual testing	20000000	1000000000			177322243499969706539110954183491697044649	42	137.025	11.18	0.727	22.35	11.615%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:30	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-21T17:05:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-28T21:50:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.089	-	-
2012-08-18T15:35:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.461	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.283	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.567	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.079	-	-
2015-04-19T11:20:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.158	-	-
2017-02-10T15:33:25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.316	-	-
2019-02-11T13:34:45	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.632	-	-
2021-01-07T08:06:15	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.26	-	-

ECM factoring results:

Total ECM effort:	2.207 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-13T02:57:00	Gerry Snyder	blu	50000	5000000						3	0.441
2012-02-10T19:39:00	Lukasz Wrobel	u-w	50000	5000000						3	0.441
2015-03-02T18:02:00	Sid & Andy	Emperor_Zurg	50000	5000000						3	0.441
2016-12-25T10:33:36	Bruce	agent86	50000	5000000						3	0.441
2019-06-16T19:41:54	furkell	furkell1	50000	5000000						3	0.441

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	ANONYMOUS	v4_computers	6752CFB670B2A162	0.364

date

userid

compid

res64

spent (GHz-days)

1999-08-31T00:00:00

ANONYMOUS

v4_computers

6752CFB670B2A162

0.364

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 = 20000000, B2 = 1000000000 (stage 2)

B1 = 20000000 (stage 1)

B1 = 500000, B2 = 10000000 (stage 2)

B1 = 500000 (stage 1)

B1 = 60000, B2 = 990000 (stage 2)

B1 = 78535 (stage 1)

B1 = 60000 (stage 1)

B1 = 20000, B2 = 235000 (stage 2)

B1 = 20000 (stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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