M1465487 Mersenne number exponent details

Residue

Status

L-L

BE3D9DC11E260067

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	20.2758	68.6567%	800000	16000000	0.0901	5.2630%	20.3659	70.3063%	1.6496%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9101%	0.0073	63.5913%	1.0913%
GPU72	2⁶⁰	0.1048	65.0000%	6500	100000	0.0006	1.4461%	0.1054	65.5061%	0.5061%
Difference	+7	+20.1710	+3.6567%	+793500	+15900000	+0.0895	+3.8169%	+20.2605	+4.8002%	+4.8002%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.2758

68.6567%

800000

16000000

0.0901

5.2630%

20.3659

70.3063%

1.6496%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9101%

0.0073

63.5913%

1.0913%

GPU72

2⁶⁰

0.1048

65.0000%

6500

100000

0.0006

1.4461%

0.1054

65.5061%

0.5061%

Difference

+20.1710

+3.6567%

+793500

+15900000

+0.0895

+3.8169%

+20.2605

+4.8002%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1465487	461179660412822798801	21	68.644	157346895746200 2³ × 5² × 6221 × 126464311	2014-11-29	6221	126464311	42.085	0.3818	0.7124

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1465487

461179660412822798801

68.644

157346895746200
2³ × 5² × 6221 × 126464311

2014-11-29

6221

126464311

42.085

0.3818

0.7124

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	265000		-		-	-	0.002	-	-	0.956%
2009-04-13T05:55:00	axn	Manual testing	800000	16000000		-		-	-	0.090	-	-	5.263%
2016-03-17T19:14:41	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.934%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2010-05-07T04:20:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.105	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.089	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.582 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.582 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	11.86
50000	5000000	461179660412822798801	1	0.047
250000	35000000		50	13.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T22:03:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-12-17T22:03:00	Nathan Slaven	q6600	50000	5000000						3	0.142
2009-06-22T18:19:00	SubPrime	abd1	50000	5000000						3	0.142
2010-05-05T06:41:00	Wojciech Florek	perta	50000	5000000						3	0.142
2011-08-16T22:42:00	Andrew B	dell_xps_17	50000	5000000						3	0.142
2012-11-30T02:17:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.142
2013-09-18T12:02:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2014-03-15T19:39:00	Sara	Sara	50000	5000000						3	0.142
2014-11-29T00:42:00	Chang Chia-Tche	exbpc13	50000	5000000	461179660412822798801	68.644	1	2		1	0.047
2019-04-12T15:23:51	TJAOI	Manual testing	50000	5000000						228	10.81
2022-01-25T11:44:09	TJAOI	Manual testing	250000	35000000						50	13.68

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	BE3D9DC11E260067	0.056

date

userid

compid

res64

spent (GHz-days)

1999-01-10T00:00:00

ANONYMOUS

v4_computers

BE3D9DC11E260067

0.056

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 = 800000, B2 = 16000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 800000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

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