M1521769 Mersenne number exponent details

Residue

Status

L-L

2DED58822956EDA7

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	19.5259	68.6567%	500000	15000000	0.0835	4.9570%	19.6095	70.2104%	1.5537%
PrimeNet	2⁵⁷	0.0126	63.1579%	6500	110000	0.0008	2.4117%	0.0134	64.0464%	0.8885%
GPU72	2⁶¹	0.2019	65.5738%	6500	55000	0.0006	1.0130%	0.2024	65.9225%	0.3487%
Difference	+6	+19.3240	+3.0829%	+493500	+14945000	+0.0830	+3.9440%	+19.4070	+4.2879%	+4.2879%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.5259

68.6567%

500000

15000000

0.0835

4.9570%

19.6095

70.2104%

1.5537%

PrimeNet

2⁵⁷

0.0126

63.1579%

6500

110000

0.0008

2.4117%

0.0134

64.0464%

0.8885%

GPU72

2⁶¹

0.2019

65.5738%

6500

55000

0.0006

1.0130%

0.2024

65.9225%

0.3487%

Difference

+19.3240

+3.0829%

+493500

+14945000

+0.0830

+3.9440%

+19.4070

+4.2879%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1521769	71158028933598788927	20	65.948	23380036304327 53 × 15629 × 28225271	2013-08-08	15629	28225271	8.1604	0.1006	0.1860

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1521769

71158028933598788927

65.948

23380036304327
53 × 15629 × 28225271

2013-08-08

15629

28225271

8.1604

0.1006

0.1860

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-29T11:48:00	James Heinrich	WHS	80000	1340000		-		-	-	0.010	-	-	2.191%
2016-03-17T19:15:50	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	4.957%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1998-12-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.025	-	-
2010-04-25T12:20:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.101	-	-
2010-05-04T02:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.049	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.948 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	13.948 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.065	0.031%
25	50000	0.729	48.246%
30	250000	0.045	95.611%
35	1000000	0.002	99.795%

ECM Summary

B1	B2	factor	curves	GHz-days
		71158028933598788927	1	0.00000e+0
50000	5000000		250	13.95

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-21T11:21:00	Steve Scott	Abit-3	50000	5000000						3	0.167
2009-04-10T16:50:00	Aca Arsov	backo6400	50000	5000000						3	0.167
2010-02-06T23:50:00	James Hintz	ryan	50000	5000000						3	0.167
2011-04-05T19:45:00	Beat Bucheli	I7	50000	5000000						3	0.167
2012-10-19T16:10:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.167
2013-08-08T12:54:00	Chang Chia-Tche	exbpc13			71158028933598788927	65.948		1		1	-
2019-06-07T09:13:57	TJAOI	Manual testing	50000	5000000						235	13.11

date	userid	compid	res64	spent (GHz-days)
1997-11-12T00:00:00	ANONYMOUS	v4_computers	2DED58822956EDA7	0.068
1999-02-14T00:00:00	ANONYMOUS	v4_computers	2DED58822956EDA7	0.068

date

userid

compid

res64

spent (GHz-days)

1997-11-12T00:00:00

ANONYMOUS

v4_computers

2DED58822956EDA7

0.068

1999-02-14T00:00:00

ANONYMOUS

v4_computers

2DED58822956EDA7

0.068

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T13:31:24

Oliver Kruse

GTX-1

71158028933598788927

791B2F4D1C282B__

2017-10-29T21:25:46

kkmrkkblmbrbk

c4.xlarge

71158028933598788927

791B2F4D1C282B__

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 = 80000, B2 = 1340000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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