M1481483 Mersenne number exponent details

Residue

Status

L-L

737D6656E886FD8C

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	20.0569	68.6567%	500000	15000000	0.0714	4.9410%	20.1283	70.2054%	1.5487%
PrimeNet	2⁵⁷	0.0130	63.1579%	6500	100000	0.0006	2.3346%	0.0136	64.0180%	0.8601%
GPU72	2⁶¹	0.2073	65.5738%	6000	50000	0.0005	0.9453%	0.2078	65.8992%	0.3254%
Difference	+6	+19.8495	+3.0829%	+494000	+14950000	+0.0710	+3.9957%	+19.9205	+4.3062%	+4.3062%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.0569

68.6567%

500000

15000000

0.0714

4.9410%

20.1283

70.2054%

1.5487%

PrimeNet

2⁵⁷

0.0130

63.1579%

6500

100000

0.0006

2.3346%

0.0136

64.0180%

0.8601%

GPU72

2⁶¹

0.2073

65.5738%

6000

50000

0.0005

0.9453%

0.2078

65.8992%

0.3254%

Difference

+19.8495

+3.0829%

+494000

+14950000

+0.0710

+3.9957%

+19.9205

+4.3062%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1481483	741619431876329621233	21	69.329	250296301704552 2³ × 3 × 1465727 × 7115249	2014-08-27	1465727	7115249	132.15	0.0982	0.1651

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1481483

741619431876329621233

69.329

250296301704552
2³ × 3 × 1465727 × 7115249

2014-08-27

1465727

7115249

132.15

0.0982

0.1651

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	270000		-		-	-	0.002	-	-	0.963%
2010-12-18T11:21:00	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.221%
2010-12-19T12:32:00	Rob_Dee	twopc	200000	300000		-		-	-	0.011	-	-	1.524%
2010-12-20T11:46:00	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.340%
2010-12-21T11:48:00	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.828%
2010-12-22T11:36:00	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	3.120%
2010-12-23T11:58:00	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	3.330%
2010-12-24T12:21:00	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.495%
2016-03-17T19:14:54	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.941%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2010-05-06T08:20:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.104	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.077	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.927 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:	11.927 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		250	11.88
50000	5000000	741619431876329621233	1	0.048

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-09T10:34:00	Steve Scott	Abit-3	50000	5000000						3	0.143
2009-03-11T18:35:00	Sturle Sunde	FLB-ST-0033	50000	5000000						3	0.143
2010-01-11T17:35:00	sannerud.com	strs-w2k8e	50000	5000000						3	0.143
2011-04-12T08:47:00	Lupo	yorick	50000	5000000						3	0.143
2012-07-23T19:07:00	vichico	NEO3	50000	5000000						3	0.143
2013-06-10T10:16:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.143
2014-01-26T15:47:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.143
2014-08-27T18:24:00	Chang Chia-Tche	exbpc13	50000	5000000	741619431876329621233	69.329	1	2		1	0.048
2019-05-03T14:21:14	TJAOI	Manual testing	50000	5000000						229	10.88

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	737D6656E886FD8C	0.057

date

userid

compid

res64

spent (GHz-days)

1998-11-21T00:00:00

ANONYMOUS

v4_computers

737D6656E886FD8C

0.057

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 200000, B2 = 4000000 (P-1 stage 2)

B1 = 200000, B2 = 3000000 (P-1 stage 2)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 200000, B2 = 1000000 (P-1 stage 2)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 20000, B2 = 270000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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