M1609567 Mersenne number exponent details

Residue

Status

L-L

461F1E5CEF1AC12A

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	18.4608	68.6567%	10000000	200000000	1.3181	9.7559%	19.7789	71.7145%	3.0578%
PrimeNet	2⁵⁷	0.0119	63.1579%	7000	120000	0.0009	2.5511%	0.0128	64.0978%	0.9399%
GPU72	2⁶¹	0.1908	65.5738%	6500	60000	0.0006	1.0577%	0.1915	65.9379%	0.3641%
Difference	+6	+18.2700	+3.0829%	+9993500	+199940000	+1.3175	+8.6981%	+19.5875	+5.7766%	+5.7766%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.4608

68.6567%

10000000

200000000

1.3181

9.7559%

19.7789

71.7145%

3.0578%

PrimeNet

2⁵⁷

0.0119

63.1579%

7000

120000

0.0009

2.5511%

0.0128

64.0978%

0.9399%

GPU72

2⁶¹

0.1908

65.5738%

6500

60000

0.0006

1.0577%

0.1915

65.9379%

0.3641%

Difference

+18.2700

+3.0829%

+9993500

+199940000

+1.3175

+8.6981%

+19.5875

+5.7766%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1609567	3952519545387134687707793	25	81.709	1227820757193436088 2³ × 431² × 1451 × 569407301	2017-01-09	185761	569407301	577,443	2.0206	3.7527

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1609567

3952519545387134687707793

81.709

1227820757193436088
2³ × 431² × 1451 × 569407301

2017-01-09

185761

569407301

577,443

2.0206

3.7527

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-11-16T10:21:00	BigBrother	Winston	100000	2000000		-		-	-	0.013	-	-	2.550%
2014-04-25T23:37:00	ANONYMOUS	Manual testing	150000	150000		-		-	-	0.010	-	-	1.098%
2014-09-18T20:49:00	Jocelyn Larouche	Manual testing	189877	189877		-		-	-	0.012	-	-	1.243%
2015-02-15T11:05:00	VictordeHollander	Manual testing	10000000	200000000		-		-	-	1.318	-	-	9.756%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.072	-	-
2010-05-04T13:20:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.095	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.191	-	-
2010-07-12T02:44:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.992	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.610	-	-
2015-01-30T19:14:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	1.220	-	-
2015-01-30T19:14:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	2.321	-	-
2015-10-11T16:52:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.643	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.652 GHz-days
Estimated T-Level:	24.982

Digits	B1	Curves	Complete	FacMiss
20	11000	279 / 100	2.790	6.056%
25	50000	279 / 280	0.996	36.854%

New Calculation Method

Total ECM effort:	15.652 GHz-days
Estimated T-Level:	24.982

Digits	B1	Complete	FacMiss
20	11000	9.000	0.012%
25	50000	0.813	44.334%
30	250000	0.050	95.114%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		277	15.54
50000	5000000	3952519545387134687707793	2	0.112

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-04-05T00:33:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.168
2010-04-05T07:02:00	unconnected	X3220--xp	50000	5000000						3	0.168
2010-04-09T04:42:00	SubPrime	stor	50000	5000000						3	0.168
2011-08-27T16:00:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.168
2013-02-03T09:11:00	butera	Backup	50000	5000000						3	0.168
2013-11-02T17:59:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2014-04-19T20:02:00	mikr	MSI	50000	5000000						12	0.673
2016-03-20T22:57:12	Bruce	DESK3	50000	5000000						3	0.168
2016-04-30T22:53:30	Bruce	DESK3	50000	5000000						3	0.168
2016-07-24T13:22:36	Bruce	DESK3	50000	5000000						3	0.168
2016-09-23T10:24:48	Bruce	DESK3	50000	5000000						3	0.168
2016-11-19T07:22:30	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2017-01-09T16:22:31	Chang Chia-Tche	exbpc13	50000	5000000	3952519545387134687707793	81.709	2	2		2	0.112
2017-03-23T15:08:01	VictordeHollander	Manual testing	50000	5000000						232	13.01

date	userid	compid	res64	spent (GHz-days)
2015-07-20T14:32:00	MadPoo	Manual testing	461F1E5CEF1AC12A	0.072

date

userid

compid

res64

spent (GHz-days)

2015-07-20T14:32:00

MadPoo

Manual testing

461F1E5CEF1AC12A

0.072

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 = 10000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 100000, B2 = 2000000 (P-1 stage 2)

B1 = 189877 (P-1 stage 1)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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