M1615591 Mersenne number exponent details

Residue

Status

L-L

CD930511B715E436

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	18.3920	68.6567%	1000000	20000000	0.1318	5.6741%	18.5238	70.4352%	1.7785%
PrimeNet	2⁵⁷	0.0119	63.1579%	7000	120000	0.0009	2.5529%	0.0127	64.0984%	0.9406%
GPU72	2⁶¹	0.1901	65.5738%	6500	60000	0.0006	1.0586%	0.1907	65.9382%	0.3644%
Difference	+6	+18.2018	+3.0829%	+993500	+19940000	+0.1312	+4.6155%	+18.3330	+4.4970%	+4.4970%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.3920

68.6567%

1000000

20000000

0.1318

5.6741%

18.5238

70.4352%

1.7785%

PrimeNet

2⁵⁷

0.0119

63.1579%

7000

120000

0.0009

2.5529%

0.0127

64.0984%

0.9406%

GPU72

2⁶¹

0.1901

65.5738%

6500

60000

0.0006

1.0586%

0.1907

65.9382%

0.3644%

Difference

+18.2018

+3.0829%

+993500

+19940000

+0.1312

+4.6155%

+18.3330

+4.4970%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1615591	1267349174929877292370057	25	80.068	392224633254913308 2² × 3 × 8849 × 3693681331741	2016-11-22	8849	3693681331741	265,337	13,034	24,343

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1615591

1267349174929877292370057

80.068

392224633254913308
2² × 3 × 8849 × 3693681331741

2016-11-22

8849

3693681331741

265,337

13,034

24,343

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-11-23T13:31:00	BigBrother	Winston	1000000	20000000		-		-	-	0.132	-	-	5.674%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-11-23T13:31:00

BigBrother

Winston

1000000

20000000

0.132

-

-

5.674%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	Dry Creek Photo	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.071	-	-
2010-05-01T01:40:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.095	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.190	-	-
2010-07-24T22:47:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.988	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.608	-	-
2015-04-26T11:20:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.215	-	-
2015-04-27T10:26:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.313	-	-
2015-10-11T16:52:29	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.625	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.086 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.086 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	13.92
50000	5000000	1267349174929877292370057	3	0.168

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-04-18T22:19:00	Matt	HP	50000	5000000						3	0.168
2009-05-26T08:56:00	Lupo	yorick	50000	5000000						3	0.168
2010-04-13T10:07:00	SubPrime	stor	50000	5000000						3	0.168
2011-08-29T05:56:00	S36049	Wolle5	50000	5000000						3	0.168
2013-02-19T13:47:00	OS1	L3	50000	5000000						3	0.168
2013-11-05T11:36:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2014-05-10T21:14:00	mikr	MSI	50000	5000000						12	0.673
2016-03-23T07:55:54	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2016-05-03T21:08:30	Bruce	DESK3	50000	5000000						3	0.168
2016-07-27T14:35:10	Bruce	DESK3	50000	5000000						3	0.168
2016-09-26T03:08:17	Bruce	DESK3	50000	5000000						3	0.168
2016-11-22T08:45:05	Bruce	DESK3	50000	5000000	1267349174929877292370057	80.068	3	2		3	0.168
2019-10-07T13:18:27	TJAOI	Manual testing	50000	5000000						206	11.56

date	userid	compid	res64	spent (GHz-days)
1998-11-14T00:00:00	Dry Creek Photo	v4_computers	CD930511B715E436	0.072
2015-07-19T18:02:00	MadPoo	Manual testing	CD930511B715E436	0.072

date

userid

compid

res64

spent (GHz-days)

1998-11-14T00:00:00

Dry Creek Photo

v4_computers

CD930511B715E436

0.072

2015-07-19T18:02:00

MadPoo

Manual testing

CD930511B715E436

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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