M9293941 Mersenne number exponent details

Residue

Status

L-L

DA243ED646234929

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	3.1971	64.1791%	175000	3806250	0.1494	4.1477%	3.3465	65.6648%	1.4857%
PrimeNet	2⁶⁴	0.3830	62.5000%	40000	1100000	0.0392	3.4887%	0.4221	63.8083%	1.3083%
GPU72	2⁶⁸	6.4133	64.7059%	60000	1400000	0.0533	2.4554%	6.4666	65.5725%	0.8666%
Difference	-1	-3.2162	-0.5268%	+115000	+2406250	+0.0961	+1.6923%	-3.1201	+0.0923%	+0.0923%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.1971

64.1791%

175000

3806250

0.1494

4.1477%

3.3465

65.6648%

1.4857%

PrimeNet

2⁶⁴

0.3830

62.5000%

40000

1100000

0.0392

3.4887%

0.4221

63.8083%

1.3083%

GPU72

2⁶⁸

6.4133

64.7059%

60000

1400000

0.0533

2.4554%

6.4666

65.5725%

0.8666%

Difference

-1

-3.2162

-0.5268%

+115000

+2406250

+0.0961

+1.6923%

-3.1201

+0.0923%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9293941	369774973850191699915534609	27	88.257	19893335553248707944 2³ × 3³ × 67 × 1374608592678877	2014-07-08	67	1374608592678877	8,444,154	30,014,197	56,058,161

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9293941

369774973850191699915534609

88.257

19893335553248707944
2³ × 3³ × 67 × 1374608592678877

2014-07-08

1374608592678877

8,444,154

30,014,197

56,058,161

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-10T00:00:00	ANONYMOUS	v4_computers	40000	290000		-		-	-	0.021	-	-	1.670%
2012-07-06T12:10:00	Squeeky_Squirrel	T7500_2200	175000	3806250		-		-	-	0.149	-	-	4.148%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.383	-	-
2013-09-07T07:14:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.402	-	-

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	369774973850191699915534609	3	1.261

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-07-08T17:32:00	swildner	gamebox	50000	5000000	369774973850191699915534609	88.257	3	2		3	1.261

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-03-15T00:00:00	davidcross	v4_computers	DA243ED646234929	2.569
2003-05-04T00:00:00	ANONYMOUS	v4_computers	DA243ED646234929	2.569

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-08-22T05:02:00

mnd9

libproj

369774973850191699915534609

CEDEAB91411B51__

2020-11-11T12:42:01

kutens

spica-b

369774973850191699915534609

CEDEAB91411B5120

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 = 3806250 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 40000, B2 = 290000 (P-1 stage 2)

B1 = 40000 (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

10¹⁵

10¹⁶

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