M4422391 Mersenne number exponent details

Residue

Status

L-L

4984AFBADE5046F5

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	6.7190	65.6716%	1800000	68000000	0.9778	8.1983%	7.6968	68.4860%	2.8143%
PrimeNet	2⁶¹	0.0695	62.2951%	18000	360000	0.0066	2.9401%	0.0761	63.4036%	1.1086%
GPU72	2⁶⁵	1.6497	64.6154%	26000	500000	0.0094	2.0336%	1.6591	65.3350%	0.7196%
Difference	+2	+5.0693	+1.0563%	+1774000	+67500000	+0.9684	+6.1647%	+6.0377	+3.1510%	+3.1510%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.7190

65.6716%

1800000

68000000

0.9778

8.1983%

7.6968

68.4860%

2.8143%

PrimeNet

2⁶¹

0.0695

62.2951%

18000

360000

0.0066

2.9401%

0.0761

63.4036%

1.1086%

GPU72

2⁶⁵

1.6497

64.6154%

26000

500000

0.0094

2.0336%

1.6591

65.3350%

0.7196%

Difference

+5.0693

+1.0563%

+1774000

+67500000

+0.9684

+6.1647%

+6.0377

+3.1510%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4422391	46353550780188665719441958449	29	95.227	5240779340880155748264 2³ × 3² × 31 × 149 × 18211 × 170539 × 5074087	2016-09-17	170539	5074087	1.894e+9	0.0792	0.0934

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4422391

46353550780188665719441958449

95.227

5240779340880155748264
2³ × 3² × 31 × 149 × 18211 × 170539 × 5074087

2016-09-17

170539

5074087

1.894e+9

0.0792

0.0934

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-19T08:37:00	Carsten Kossendey	durandal	25000	356250		-		-	-	0.008	-	-	1.385%
2012-04-02T16:00:00	Squeeky_Squirrel	T7500_2200	135000	2733750		-		-	-	0.050	-	-	3.352%
2016-09-17T08:07:54	mikr	MSI	1800000	68000000	12		46353550780188665719441958449	29	95.227	0.978	1.103	1.956	8.198%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.035	-	-
2001-11-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.069	-	-
2010-10-21T21:38:00	markr	ut	2⁶¹	2⁶²		-	-	0.069	-	-
2012-01-14T04:25:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.361	-	-
2016-02-23T16:38:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.222	-	-
2014-08-27T15:42:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.444	-	-
2014-08-30T11:46:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.845	-	-
2015-06-22T11:54:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.690	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.656 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.656 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.656

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-29T09:12:00	GrunwalderGIMP	compute-0-9	50000	5000000						3	0.552
2013-04-12T19:45:00	S00030	mac399	50000	5000000						3	0.552
2016-09-10T14:26:08	ethanmyers	ethan	50000	5000000						3	0.552

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-23T00:00:00	ANONYMOUS	v4_computers	4984AFBADE5046F5	0.552
1999-11-10T00:00:00	ANONYMOUS	v4_computers	4984AFBADE5046F5	0.552

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:29:24

kkmrkkblmbrbk

Manual testing

46353550780188665719441958449

AE5D4EC2CF0BFB__

2018-02-10T22:34:24

trebor

Laptop

46353550780188665719441958449

AE5D4EC2CF0BFB__

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 = 1800000, B2 = 68000000 (P-1 stage 2)

B1 = 1800000 (P-1 stage 1)

B1 = 135000, B2 = 2733750 (P-1 stage 2)

B1 = 135000 (P-1 stage 1)

B1 = 25000, B2 = 356250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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