M9328027 Mersenne number exponent details

Residue

Status

L-L

3D62B70D828FDB2E

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	3.1854	64.1791%	175000	3850000	0.1504	4.1597%	3.3358	65.6691%	1.4900%
PrimeNet	2⁶⁴	0.3816	62.5000%	40000	1100000	0.0392	3.4907%	0.4207	63.8090%	1.3090%
GPU72	2⁶⁸	6.3899	64.7059%	60000	1400000	0.0533	2.4568%	6.4432	65.5730%	0.8671%
Difference	-1	-3.2044	-0.5268%	+115000	+2450000	+0.0971	+1.7028%	-3.1074	+0.0961%	+0.0961%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.1854

64.1791%

175000

3850000

0.1504

4.1597%

3.3358

65.6691%

1.4900%

PrimeNet

2⁶⁴

0.3816

62.5000%

40000

1100000

0.0392

3.4907%

0.4207

63.8090%

1.3090%

GPU72

2⁶⁸

6.3899

64.7059%

60000

1400000

0.0533

2.4568%

6.4432

65.5730%

0.8671%

Difference

-1

-3.2044

-0.5268%

+115000

+2450000

+0.0971

+1.7028%

-3.1074

+0.0961%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9328027	29787871573504705480927	23	74.657	1596686607655869 3 × 23 × 3499 × 6613428299	2014-07-19	3499	6613428299	522.81	144.40	269.70

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9328027

29787871573504705480927

74.657

1596686607655869
3 × 23 × 3499 × 6613428299

2014-07-19

3499

6613428299

522.81

144.40

269.70

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-08T00:00:00	Dr. Nowak	v4_computers	125000	125000		-		-	-	0.050	-	-	1.355%
2012-08-16T17:40:00	James Heinrich	i7-920	175000	3850000		-		-	-	0.150	-	-	4.160%

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	2⁵⁵		-	-	0.001	-	-
1999-02-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.066	-	-
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.382	-	-
2013-09-06T00:59:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.401	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.261 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	1.261 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	29787871573504705480927	3	1.261

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-07-19T09:47:00	swildner	gamebox	50000	5000000	29787871573504705480927	74.657	3	2		3	1.261

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-03-15T00:00:00	ANONYMOUS	v4_computers	F9B43FE03A1916__	2.578
2001-05-20T00:00:00	Dr. Nowak	v4_computers	3D62B70D828FDB2E	2.578
2003-04-19T00:00:00	shaneamy	v4_computers	97021D1598FF3F__	2.578
2003-06-17T00:00:00	ANONYMOUS	v4_computers	3D62B70D828FDB2E	2.578

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-08-26T14:18:24

mnd9

25836b

29787871573504705480927

7B66A0C89B8FC3__

2020-11-13T22:13:42

oodaira

com2

29787871573504705480927

7B66A0C89B8FC387

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 = 175000, B2 = 3850000 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 125000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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