M1595653 Mersenne number exponent details

Residue

Status

L-L

717187AA2F502B9E

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	18.6218	68.6567%	10000000	200000000	1.3181	9.7485%	19.9399	71.7122%	3.0555%
PrimeNet	2⁵⁷	0.0120	63.1579%	7000	120000	0.0009	2.5468%	0.0129	64.0962%	0.9383%
GPU72	2⁶¹	0.1925	65.5738%	6500	60000	0.0006	1.0557%	0.1931	65.9372%	0.3634%
Difference	+6	+18.4293	+3.0829%	+9993500	+199940000	+1.3175	+8.6928%	+19.7468	+5.7750%	+5.7750%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.6218

68.6567%

10000000

200000000

1.3181

9.7485%

19.9399

71.7122%

3.0555%

PrimeNet

2⁵⁷

0.0120

63.1579%

7000

120000

0.0009

2.5468%

0.0129

64.0962%

0.9383%

GPU72

2⁶¹

0.1925

65.5738%

6500

60000

0.0006

1.0557%

0.1931

65.9372%

0.3634%

Difference

+18.4293

+3.0829%

+9993500

+199940000

+1.3175

+8.6928%

+19.7468

+5.7750%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1595653	2493038754219215939122681	25	81.044	781197025361784780 2² × 3 × 5 × 7 × 6762121 × 275060579	2017-01-02	6762121	275060579	474,327	1.3847	1.8128

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1595653

2493038754219215939122681

81.044

781197025361784780
2² × 3 × 5 × 7 × 6762121 × 275060579

2017-01-02

6762121

275060579

474,327

1.3847

1.8128

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-04T14:44:00	James Heinrich	WHS	85000	1445000		-		-	-	0.010	-	-	2.278%
2013-12-05T22:06:00	David Campeau	i5-2500k	980000	28420000		-		-	-	0.160	-	-	6.028%
2015-04-21T09:17:00	VictordeHollander	Manual testing	10000000	200000000		-		-	-	1.318	-	-	9.748%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2016-02-23T16:28:40	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.072	-	-
2010-05-02T18:30:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.096	-	-
2016-02-23T16:28:40	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.193	-	-
2010-07-04T17:55:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.000	-	-
2016-02-23T16:28:40	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.615	-	-
2015-03-04T21:28:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.230	-	-
2015-03-04T21:28:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.342	-	-
2015-10-11T16:52:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.683	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.069 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:	14.069 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	13.90
50000	5000000	2493038754219215939122681	3	0.168

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-03-23T14:54:00	Scott Kurowski	UW1	50000	5000000						3	0.168
2009-05-16T23:25:00	S36049	Wolle3	50000	5000000						3	0.168
2010-03-24T06:48:00	James Classen	towerofart	50000	5000000						3	0.168
2011-08-13T21:30:00	S36049	Wolle5	50000	5000000						3	0.168
2013-03-09T10:25:00	Smurgs	Praca	50000	5000000						3	0.168
2013-10-28T19:28:00	arnaud	SPR14	50000	5000000						3	0.168
2014-06-06T20:14:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-03-12T01:58:00	codest	aliyun	50000	5000000						3	0.168
2015-10-04T11:22:28	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2016-01-13T01:13:01	Adel El-Atawy	AE2MTV	50000	5000000						3	0.168
2016-01-13T02:26:28	Adel El-Atawy	AE2MTV	50000	5000000						3	0.168
2016-04-24T17:53:44	Bruce	DESK3	50000	5000000						3	0.168
2016-06-23T04:09:29	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2016-09-13T03:14:43	Bruce	DESK3	50000	5000000						3	0.168
2016-11-12T03:13:40	Bruce	DESK3	50000	5000000						3	0.168
2017-01-02T22:12:39	Bruce	DESK3	50000	5000000	2493038754219215939122681	81.044	3	2		3	0.168
2019-09-02T12:32:18	TJAOI	Manual testing	50000	5000000						203	11.38

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	717187AA2F502B9E	0.071
2015-07-10T01:00:00	MadPoo	Manual testing	717187AA2F502B9E	0.071

date

userid

compid

res64

spent (GHz-days)

1999-03-26T00:00:00

ANONYMOUS

v4_computers

717187AA2F502B9E

0.071

2015-07-10T01:00:00

MadPoo

Manual testing

717187AA2F502B9E

0.071

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 = 980000, B2 = 28420000 (P-1 stage 2)

B1 = 980000 (P-1 stage 1)

B1 = 85000, B2 = 1445000 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

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