M9090017 Mersenne number exponent details

Residue

Status

L-L

80444A61A619E237

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	3.2689	64.1791%	50000	550000	0.0310	2.1023%	3.2998	64.9322%	2.4322%
PrimeNet	2⁶⁴	0.3916	62.5000%	36000	1000000	0.0355	3.3319%	0.4270	63.7495%	1.2495%
GPU72	2⁶⁸	6.5572	64.7059%	60000	1300000	0.0511	2.4037%	6.6083	65.5542%	0.8484%
Difference	-1	-3.2883	-0.5268%	-10000	-750000	-0.0202	-0.3014%	-3.3085	-0.6221%	-0.6221%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.2689

64.1791%

50000

550000

0.0310

2.1023%

3.2998

64.9322%

2.4322%

PrimeNet

2⁶⁴

0.3916

62.5000%

36000

1000000

0.0355

3.3319%

0.4270

63.7495%

1.2495%

GPU72

2⁶⁸

6.5572

64.7059%

60000

1300000

0.0511

2.4037%

6.6083

65.5542%

0.8484%

Difference

-1

-3.2883

-0.5268%

-10000

-750000

-0.0202

-0.3014%

-3.3085

-0.6221%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9090017	516770062491225473521	21	68.808	28425142796280 2³ × 3 × 5 × 61 × 97 × 389 × 102913	2012-11-15	389	102913	12.365	0.0024	0.0042

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9090017

516770062491225473521

68.808

28425142796280
2³ × 3 × 5 × 61 × 97 × 389 × 102913

2012-11-15

389

102913

12.365

0.0024

0.0042

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-04-10T00:00:00	ANONYMOUS	v4_computers	50000	550000		-		-	-	0.031	-	-	2.102%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-04-10T00:00:00

ANONYMOUS

v4_computers

50000

550000

0.031

-

-

2.102%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁵		-	-	0.001	-	-
1998-12-21T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.034	-	-
1999-01-02T00:00:00	ANONYMOUS	v4_computers	?	2⁶³		-	-	0.108	-	-
2007-04-07T00:00:00	ANONYMOUS	v4_computers	?	2⁶⁴		-	-	0.216	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.109 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	16.109 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	1.094	33.503%
25	50000	0.104	90.146%
30	250000	0.007	99.311%

ECM Summary

B1	B2	factor	curves	GHz-days
		516770062491225473521	1	0.00000e+0
50000	4650000		6	2.434
50000	5650000		6	2.685
50000	5750000		6	2.710
75000	7725000		6	3.839
75000	10125000		6	4.441

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-11-15T12:49:00	Stef42	Manual testing			516770062491225473521	68.808		1		1	-
2020-12-22T23:16:11	masser	Manual testing	50000	5650000						6	2.685
2020-12-22T23:17:17	masser	Manual testing	75000	10125000						6	4.441
2020-12-22T23:20:05	masser	Manual testing	50000	4650000						6	2.434
2020-12-22T23:23:11	masser	Manual testing	50000	5750000						6	2.710
2020-12-22T23:24:37	masser	Manual testing	75000	7725000						6	3.839

date	userid	compid	res64	spent (GHz-days)
2000-08-10T00:00:00	ANONYMOUS	v4_computers	80444A61A619E237	2.512
2003-05-26T00:00:00	ANONYMOUS	v4_computers	80444A61A619E237	2.512

date

userid

compid

res64

spent (GHz-days)

2000-08-10T00:00:00

ANONYMOUS

v4_computers

80444A61A619E237

2.512

2003-05-26T00:00:00

ANONYMOUS

v4_computers

80444A61A619E237

2.512

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-06-13T14:21:38

Niels_Mache_Nextcloud

SuperDry-X

516770062491225473521

3D03D46FD39104__

2020-10-17T00:26:03

kutens

hadar

516770062491225473521

3D03D46FD391048A

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 = 550000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

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