M2112007 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	14.0690	67.1642%	500000	15000000	0.1230	5.1567%	14.1920	68.8574%	1.6933%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6806%	0.0198	63.0858%	1.0168%
GPU72	2⁶²	0.2909	64.5161%	10000	140000	0.0016	1.4530%	0.2925	65.0317%	0.5156%
Difference	+5	+13.7782	+2.6481%	+490000	+14860000	+0.1214	+3.7037%	+13.8995	+3.8257%	+3.8257%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0690

67.1642%

500000

15000000

0.1230

5.1567%

14.1920

68.8574%

1.6933%

PrimeNet

2⁵⁸

0.0182

62.0690%

9000

160000

0.0016

2.6806%

0.0198

63.0858%

1.0168%

GPU72

2⁶²

0.2909

64.5161%

10000

140000

0.0016

1.4530%

0.2925

65.0317%

0.5156%

Difference

+13.7782

+2.6481%

+490000

+14860000

+0.1214

+3.7037%

+13.8995

+3.8257%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2112007	238736493920167	15	47.762	56518869 3 × 11 × 37 × 41 × 1129	-	41	1129	1.351e-5	9.560e-6	1.091e-5
2112007	8802344295294122998343	22	72.898	2083881420680453 107 × 19475527296079	2021-10-04	107	19475527296079	846.20	101,161	188,940
2112007	928177224903983404337777	24	79.619	219738198051422984 2³ × 373 × 73638806317501	2019-09-18	373	73638806317501	60,028	382,498	714,400

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2112007

238736493920167

47.762

56518869
3 × 11 × 37 × 41 × 1129

1129

1.351e-5

9.560e-6

1.091e-5

2112007

8802344295294122998343

72.898

2083881420680453
107 × 19475527296079

2021-10-04

107

19475527296079

846.20

101,161

188,940

2112007

928177224903983404337777

79.619

219738198051422984
2³ × 373 × 73638806317501

2019-09-18

373

73638806317501

60,028

382,498

714,400

exponent	prime factors	composite factor	digits	bits*
2112007	238736493920167 8802344295294122998343	2101440815336702071302959908115283281	37	120.661
2112007	238736493920167 928177224903983404337777	221589776410127312190025565615340248759	39	127.381
2112007	8802344295294122998343 928177224903983404337777	8170135500655508510329754278100354483583303511	46	152.517
2112007	238736493920167 8802344295294122998343 928177224903983404337777	19505095042791843761194571093300243362842728376661 24564806337	61	200.280

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-20T18:59:40	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 238736493920167	-	-	0.123	-	-	5.157%

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.533 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	1.533 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.255
50000	5000000	8802344295294122998343	14	1.192
50000	5000000	928177224903983404337777	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-07T14:11:20	Oliver Kruse	ECM-HTC	50000	5000000						3	0.255
2019-09-18T18:27:46	Yuji HASEGAWA	sx1w7	50000	5000000	928177224903983404337777	79.619	1	2	2863241631752313	1	0.085
2021-10-04T07:42:52	MarkS	desktop-i7	50000	5000000	8802344295294122998343	72.898	14	2	5706956219882991	14	1.192

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T04:14:36

Oliver Kruse

GTX-2

238736493920167

600F9D69AC5228__

2017-11-17T11:41:12

kkmrkkblmbrbk

c4.xlarge

238736493920167

600F9D69AC5228__

2019-09-19T10:13:04

mnd9

75202b

238736493920167

928177224903983404337777

4FB970622715712A

2019-09-19T11:35:14

Igvan28

MineOld

238736493920167

928177224903983404337777

4FB970622715712A

2021-10-04T09:21:40

SRJ2877

LTOS

238736493920167

8802344295294122998343

928177224903983404337777

4FB970622715712A

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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