M9427931 Mersenne number exponent details

Residue

Status

L-L

66BC0B61E743B89F

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	3.1517	64.1791%	115000	2156250	0.0907	3.4501%	3.2423	65.4150%	1.2359%
PrimeNet	2⁶⁴	0.3775	62.5000%	40000	1100000	0.0392	3.4965%	0.4167	63.8112%	1.3112%
GPU72	2⁶⁸	6.3222	64.7059%	60000	1400000	0.0533	2.4610%	6.3755	65.5745%	0.8686%
Difference	-1	-3.1705	-0.5268%	+55000	+756250	+0.0374	+0.9891%	-3.1331	-0.1595%	-0.1595%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.1517

64.1791%

115000

2156250

0.0907

3.4501%

3.2423

65.4150%

1.2359%

PrimeNet

2⁶⁴

0.3775

62.5000%

40000

1100000

0.0392

3.4965%

0.4167

63.8112%

1.3112%

GPU72

2⁶⁸

6.3222

64.7059%

60000

1400000

0.0533

2.4610%

6.3755

65.5745%

0.8686%

Difference

-1

-3.1705

-0.5268%

+55000

+756250

+0.0374

+0.9891%

-3.1331

-0.1595%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9427931	6976834107204403540561	22	72.563	370008759461880 2³ × 3 × 5 × 7 × 11 × 157 × 255058841	2014-08-25	157	255058841	101.44	5.5692	10.402

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9427931

6976834107204403540561

72.563

370008759461880
2³ × 3 × 5 × 7 × 11 × 157 × 255058841

2014-08-25

157

255058841

101.44

5.5692

10.402

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-05-11T00:00:00	ANONYMOUS	v4_computers	50000	800000		-		-	-	0.036	-	-	2.337%
2012-12-02T01:19:00	Nesowa	Outback	115000	2156250		-		-	-	0.091	-	-	3.450%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.001	-	-
1999-04-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.378	-	-
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.378	-	-
1999-06-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.378	-	-
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.378	-	-
2013-09-03T05:46:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.396	-	-

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	6976834107204403540561	3	1.261

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-08-25T02:34:00	swildner	ultra	50000	5000000	6976834107204403540561	72.563	3	2		3	1.261

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-03-01T00:00:00	ANONYMOUS	v4_computers	66BC0B61E743B89F	2.606
2003-05-11T00:00:00	ANONYMOUS	v4_computers	66BC0B61E743B89F	2.606

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-09-14T12:09:04

mnd9

75211backdoor

6976834107204403540561

1C12F7F3F146A2__

2020-11-27T19:11:27

kutens

vega

6976834107204403540561

1C12F7F3F146A238

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 = 115000, B2 = 2156250 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 50000, B2 = 800000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

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