M6 946 171 Mersenne number exponent details

Residue

Status

L-L

1EA481F5429B66D5

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	137.6778	68.0556%	2000000	258849360	5.0569	6.9805%	142.7348	70.2854%
Target	2⁶⁷	4.2777	65.6716%	45000	900000	0.0290	2.2377%	4.3067	66.4398%
Difference	+5	+133.4001	+2.3839%	+1955000	+257949360	+5.0280	+4.7428%	+138.4281	+3.8456%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

137.6778

68.0556%

2000000

258849360

5.0569

6.9805%

142.7348

70.2854%

Target

2⁶⁷

4.2777

65.6716%

45000

900000

0.0290

2.2377%

4.3067

66.4398%

Difference

+133.4001

+2.3839%

+1955000

+257949360

+5.0280

+4.7428%

+138.4281

+3.8456%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-10	ANONYMOUS	v4_computers	35000	341250		-		-	-	0.016	-	-	0.799%
2011-12-10	James Heinrich	Q6600	130000	2827500		-		-	-	0.088	-	-	2.015%
2020-01-19	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.583%
2021-12-06	Seth_Tr	Manual testing	2000000	258849360		-		-	-	5.057	-	-	6.981%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1999-09-22	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-03-20	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.283	-	-
2014-02-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.538	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.076	-	-
2016-04-05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.152	-	-
2018-02-26	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.303	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.606	-	-
2021-07-28	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.21	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.43	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.85	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-08-29	MadPoo	IntLAVH03	50000	5000000						3	0.995
2017-04-15	nranks	wlaptop	50000	5000000						3	0.995

date	userid	compid	res64	spent (GHz-days)
1999-08-16	ANONYMOUS	v4_computers	1EA481F5429B66D5	1.515
2001-10-20	ANONYMOUS	v4_computers	1EA481F5429B66D5	1.515

date

userid

compid

res64

spent (GHz-days)

1999-08-16

ANONYMOUS

v4_computers

1EA481F5429B66D5

1.515

2001-10-20

ANONYMOUS

v4_computers

1EA481F5429B66D5

1.515

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 = 2000000, B2 = 258849360 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 600000, B2 = 12000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 130000, B2 = 2827500 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 35000, B2 = 341250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.8

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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