M1447861 Mersenne number exponent details

Residue

Status

L-L

B386A3830E533635

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	20.5226	68.6567%	500000	15000000	0.0714	4.9273%	20.5940	70.2011%	1.5444%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9033%	0.0074	63.5888%	1.0888%
GPU72	2⁶⁰	0.1061	65.0000%	6500	90000	0.0006	1.3960%	0.1067	65.4886%	0.4886%
Difference	+7	+20.4166	+3.6567%	+493500	+14910000	+0.0708	+3.5312%	+20.4874	+4.7125%	+4.7125%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.5226

68.6567%

500000

15000000

0.0714

4.9273%

20.5940

70.2011%

1.5444%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9033%

0.0074

63.5888%

1.0888%

GPU72

2⁶⁰

0.1061

65.0000%

6500

90000

0.0006

1.3960%

0.1067

65.4886%

0.4886%

Difference

+20.4166

+3.6567%

+493500

+14910000

+0.0708

+3.5312%

+20.4874

+4.7125%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1447861	1631992587476635543	19	60.501	563587453311 3 × 1609 × 116757293	2010-04-12	1609	116757293	0.1334	0.3523	0.6578
1447861	255801966312242563567	21	67.794	88337888206203 3 × 29445962735401	2019-03-08	3	29445962735401	40.913	88,817	165,885

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1447861

1631992587476635543

60.501

563587453311
3 × 1609 × 116757293

2010-04-12

1609

116757293

0.1334

0.3523

0.6578

1447861

255801966312242563567

67.794

88337888206203
3 × 29445962735401

2019-03-08

29445962735401

40.913

88,817

165,885

exponent	prime factors	composite factor	digits	bits*
1447861	1631992587476635543 255801966312242563567	417466912883527900200923719662469061881	39	128.295

exponent

prime factors

composite factor

digits

bits*

1447861

1631992587476635543
255801966312242563567

417466912883527900200923719662469061881

128.295

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	15000	243750		-		-	-	0.002	-	-	0.838%
2016-03-17T19:14:27	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.927%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.383 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	300 / 100	3.000	4.904%
25	50000	300 / 280	1.071	34.186%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	26.383 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.615	0.000%
25	50000	1.671	18.807%
30	250000	0.143	86.643%
35	1000000	0.010	99.006%

ECM Summary

B1	B2	factor	curves	GHz-days
		1631992587476635543	1	0.00000e+0
50000	5000000		218	10.32
50000	5000000	255801966312242563567	32	1.514
250000	40000000		50	14.55

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-05T01:54:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-12-28T00:41:00	Battlemaxx	Maxx_mom	50000	5000000						3	0.142
2009-06-26T09:46:00	James Hintz	07_060309	50000	5000000						3	0.142
2010-04-12T00:18:00	KAMCOBILL	PC01			1631992587476635543	60.501		1		1	-
2019-03-08T12:27:42	TJAOI	Manual testing	50000	5000000	255801966312242563567	67.794	32	2		32	1.514
2019-03-08T12:27:43	TJAOI	Manual testing	50000	5000000						211	9.99
2022-01-18T14:04:18	TJAOI	Manual testing	250000	40000000						50	14.55

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	B386A3830E533635	0.055

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

B386A3830E533635

0.055

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T01:13:00

Oliver Kruse

GTX-1

1631992587476635543

350DCAD3042D31__

2017-11-04T23:37:39

kkmrkkblmbrbk

c4.xlarge

1631992587476635543

350DCAD3042D31__

2019-03-09T12:23:25

trebor

Laptop

1631992587476635543

255801966312242563567

79CC273C517AB0BB

2019-03-10T02:23:10

kkmrkkblmbrbk

c5.large

1631992587476635543

255801966312242563567

79CC273C517AB0BB

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 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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