M4611127 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	6.4440	65.6716%	-	-	-	-	6.4440	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0666	62.2951%	20000	400000	0.0078	3.1119%	0.0744	63.4684%	1.1733%
GPU72	2⁶⁵	1.5822	64.6154%	28000	600000	0.0113	2.1879%	1.5935	65.3896%	0.7742%
Difference	+2	+4.8618	+1.0563%	-28000	-600000	-0.0113	-2.1879%	+4.8505	+0.2821%	+0.2821%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.4440

65.6716%

6.4440

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0666

62.2951%

20000

400000

0.0078

3.1119%

0.0744

63.4684%

1.1733%

GPU72

2⁶⁵

1.5822

64.6154%

28000

600000

0.0113

2.1879%

1.5935

65.3896%

0.7742%

Difference

+4.8618

+1.0563%

-28000

-600000

-0.0113

-2.1879%

+4.8505

+0.2821%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4611127	9367818057137	13	43.091	1015784 2³ × 7 × 11 × 17 × 97	-	17	97	4.744e-7	4.078e-6	6.605e-6
4611127	979449928221745777	18	59.765	106205047944 2³ × 3 × 4129 × 1071739	2015-12-13	4129	1071739	0.0269	0.0119	0.0208
4611127	522947739690161338957249	24	78.791	56704981199841312 2⁵ × 3 × 13 × 45436683653719	2019-02-23	32	45436683653719	14,690	472,617	882,717

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4611127

9367818057137

43.091

1015784
2³ × 7 × 11 × 17 × 97

4.744e-7

4.078e-6

6.605e-6

4611127

979449928221745777

59.765

106205047944
2³ × 3 × 4129 × 1071739

2015-12-13

4129

1071739

0.0269

0.0119

0.0208

4611127

522947739690161338957249

78.791

56704981199841312
2⁵ × 3 × 13 × 45436683653719

2019-02-23

45436683653719

14,690

472,617

882,717

exponent	prime factors	composite factor	digits	bits*
4611127	9367818057137 979449928221745777	9175308723657208630010474460449	31	102.856
4611127	9367818057137 522947739690161338957249	4898879278808472816664566836682336113	37	121.882
4611127	979449928221745777 522947739690161338957249	512201126103252718618049693490507549287473	42	138.556
4611127	9367818057137 979449928221745777 522947739690161338957249	47982069579959564181806516272543647863182065875523 44801	55	181.647

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-12-13T12:34:18	TJAOI	Manual testing	2⁵⁹	2⁶⁰*	979449928221745777	59.765	18	0.010	1.267	0.021

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.392 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:	0.392 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	522947739690161338957249	2	0.392

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-02-23T16:37:50	ATH	ec2-ECMCF	50000	5000000	522947739690161338957249	78.791	2	2		2	0.392

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:11:15

kkmrkkblmbrbk

Manual testing

9367818057137

979449928221745777

AD8A8B4639ABC2__

2018-02-27T22:18:47

Oliver Kruse

GTX-7

9367818057137

979449928221745777

AD8A8B4639ABC2__

2019-02-23T17:17:27

ATH

ec2-PRPCF

9367818057137

979449928221745777

522947739690161338957249

FB57B88F75E37B26

2019-02-24T02:24:58

kkmrkkblmbrbk

c5.large

9367818057137

979449928221745777

522947739690161338957249

FB57B88F75E37B26

2019-05-13T07:18:35

Daniil Tsarkov

Manual testing

9367818057137

979449928221745777

522947739690161338957249

FB57B88F75E37B26

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

10¹²

10¹³

10¹⁴

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