M9774689 Mersenne number exponent details

Residue

Status

L-L

99B0DC9B98A59B43

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	3.0399	64.1791%	50000	5000000	0.1352	3.5119%	3.1751	65.4371%	1.2580%
PrimeNet	2⁶⁴	0.3641	62.5000%	40000	1100000	0.0413	3.5161%	0.4055	63.8185%	1.3185%
GPU72	2⁶⁸	6.0979	64.7059%	65000	1500000	0.0606	2.5587%	6.1584	65.6089%	0.9031%
Difference	-1	-3.0580	-0.5268%	-15000	+3500000	+0.0746	+0.9532%	-2.9833	-0.1718%	-0.1718%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.0399

64.1791%

50000

5000000

0.1352

3.5119%

3.1751

65.4371%

1.2580%

PrimeNet

2⁶⁴

0.3641

62.5000%

40000

1100000

0.0413

3.5161%

0.4055

63.8185%

1.3185%

GPU72

2⁶⁸

6.0979

64.7059%

65000

1500000

0.0606

2.5587%

6.1584

65.6089%

0.9031%

Difference

-1

-3.0580

-0.5268%

-15000

+3500000

+0.0746

+0.9532%

-2.9833

-0.1718%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9774689	1782325907673048696617	22	70.594	91170466276372 2² × 7 × 23 × 373 × 643 × 590267	2015-01-15	643	590267	33.935	0.0139	0.0254

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9774689

1782325907673048696617

70.594

91170466276372
2² × 7 × 23 × 373 × 643 × 590267

2015-01-15

643

590267

33.935

0.0139

0.0254

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-08-24T00:00:00	ANONYMOUS	v4_computers	105000	997500		-	MISSED FACTOR!	-	-	0.065	-	-	2.837%
2003-08-08T00:00:00	StephenVR	v4_computers	45000	303750		-		-	-	0.025	-	-	1.750%
2003-08-25T00:00:00	StephenVR	v4_computers	45000	303750		-		-	-	0.025	-	-	1.750%
unknown			50000	5000000		-	MISSED FACTOR!	-	-	0.135	-	-	3.512%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-06-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.364	-	-
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.364	-	-
2013-08-25T00:12:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.382	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.444 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.444 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1782325907673048696617	1	0.444

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-01-15T08:47:00	Sid & Andy	Woody	50000	5000000	1782325907673048696617	70.594	1	2		1	0.444

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-10-07T00:00:00	ANONYMOUS	v4_computers	99B0DC9B98A59B43	2.851
2003-08-25T00:00:00	StephenVR	v4_computers	99B0DC9B98A59B43	2.851

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-10-25T08:11:46

mnd9

75203

1782325907673048696617

1B20523F47699D__

2020-12-30T17:38:24

kutens

rigel

1782325907673048696617

1B20523F47699D73

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 = 50000, B2 = 5000000 (P-1 stage 2)

B1 = 105000, B2 = 997500 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 45000, B2 = 303750 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 45000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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