M4396199 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	6.7590	65.6716%	-	-	-	-	6.7590	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0699	62.2951%	18000	360000	0.0066	2.9371%	0.0765	63.4025%	1.1074%
GPU72	2⁶⁵	1.6595	64.6154%	26000	500000	0.0094	2.0315%	1.6689	65.3342%	0.7188%
Difference	+2	+5.0995	+1.0563%	-26000	-500000	-0.0094	-2.0315%	+5.0901	+0.3374%	+0.3374%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.7590

65.6716%

6.7590

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0699

62.2951%

18000

360000

0.0066

2.9371%

0.0765

63.4025%

1.1074%

GPU72

2⁶⁵

1.6595

64.6154%

26000

500000

0.0094

2.0315%

1.6689

65.3342%

0.7188%

Difference

+5.0995

+1.0563%

-26000

-500000

-0.0094

-2.0315%

+5.0901

+0.3374%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4396199	3822055410601	13	41.797	434700 2² × 3³ × 5² × 7 × 23	-	27	27	7.270e-8	4.883e-6	9.937e-6
4396199	8350323165762023	16	52.891	949720789 157 × 6049177	2014-08-28	157	6049177	0.0002	0.0596	0.1113
4396199	16487883329716804619479	23	73.804	1875243059938461 3 × 6907 × 90499640941	2019-01-14	6907	90499640941	629.24	891.70	1,665.4

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4396199

3822055410601

41.797

434700
2² × 3³ × 5² × 7 × 23

7.270e-8

4.883e-6

9.937e-6

4396199

8350323165762023

52.891

949720789
157 × 6049177

2014-08-28

157

6049177

0.0002

0.0596

0.1113

4396199

16487883329716804619479

73.804

1875243059938461
3 × 6907 × 90499640941

2019-01-14

6907

90499640941

629.24

891.70

1,665.4

exponent	prime factors	composite factor	digits	bits*
4396199	3822055410601 8350323165762023	31915397835967611002317405823	29	94.688
4396199	3822055410601 16487883329716804619479	63017603689702144744952502907696879	35	115.601
4396199	8350323165762023 16487883329716804619479	137679154122515712822375292537584246017	39	126.695
4396199	3822055410601 8350323165762023 16487883329716804619479	52621735594093015463039779929985404663513393382621 7	51	168.492

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-08-28T11:25:00	TJAOI	Manual testing	?	?	8350323165762023	52.891	16	3.68949e-5	1.183	7.95965e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.368 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.368 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	16487883329716804619479	2	0.368

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-01-14T19:29:16	ATH	ec2-ECMCF	50000	5000000	16487883329716804619479	73.804	2	2		2	0.368

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:25:11

kkmrkkblmbrbk

Manual testing

3822055410601

8350323165762023

19C41F5CEC4945__

2018-02-08T21:26:10

Oliver Kruse

GTX-1

3822055410601

8350323165762023

19C41F5CEC4945__

2019-01-22T14:12:24

ANONYMOUS

3822055410601

8350323165762023

16487883329716804619479

EFF50537F9B8C9B5

2019-01-23T10:51:38

kkmrkkblmbrbk

c5.large

3822055410601

8350323165762023

16487883329716804619479

EFF50537F9B8C9B5

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

10⁰

10¹

10²

10³

10⁴

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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