M4015987 Mersenne number exponent details

Residue

Status

L-L

1FE95D7212CCC3FF

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	7.3989	67.1642%	4600000	125000000	2.0182	9.4872%	9.4171	70.2794%	3.1152%
PrimeNet	2⁶¹	0.0765	63.9344%	16000	320000	0.0059	2.7299%	0.0824	64.9190%	0.9845%
GPU72	2⁶⁵	1.8167	66.1538%	22000	360000	0.0073	1.7504%	1.8240	66.7463%	0.5925%
Difference	+2	+5.5822	+1.0103%	+4578000	+124640000	+2.0109	+7.7368%	+7.5931	+3.5331%	+3.5331%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.3989

67.1642%

4600000

125000000

2.0182

9.4872%

9.4171

70.2794%

3.1152%

PrimeNet

2⁶¹

0.0765

63.9344%

16000

320000

0.0059

2.7299%

0.0824

64.9190%

0.9845%

GPU72

2⁶⁵

1.8167

66.1538%

22000

360000

0.0073

1.7504%

1.8240

66.7463%

0.5925%

Difference

+5.5822

+1.0103%

+4578000

+124640000

+2.0109

+7.7368%

+7.5931

+3.5331%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4015987	85077294284886253076854009	26	86.137	10592326903060972692 2² × 3² × 7² × 43 × 1789 × 14323 × 5449793	2017-11-13	14323	5449793	5,534,130	0.0561	0.1003
4015987	2107856332730061202797853001	28	90.768	262433161851627159500 2² × 5³ × 23 × 89 × 277 × 26249 × 35264549	2017-11-13	26249	35264549	73,247,830	0.3520	0.6490

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4015987

85077294284886253076854009

86.137

10592326903060972692
2² × 3² × 7² × 43 × 1789 × 14323 × 5449793

2017-11-13

14323

5449793

5,534,130

0.0561

0.1003

4015987

2107856332730061202797853001

90.768

262433161851627159500
2² × 5³ × 23 × 89 × 277 × 26249 × 35264549

2017-11-13

26249

35264549

73,247,830

0.3520

0.6490

exponent	prime factors	composite factor	digits	bits*
4015987	85077294284886253076854009 2107856332730061202797853001	17933071352993653224421216842695587015007227271953 1009	54	176.905

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-11-21T06:43:00	harlee	P4_2600	40000	610000		-		-	-	0.013	-	-	1.793%
2013-06-19T15:02:00	Squeeky_Squirrel	P4_2600	120000	2280000		-		-	-	0.043	-	-	3.112%
2015-01-03T13:21:00	Nesowa	newfs	225000	4556250		-		-	-	0.083	-	-	3.988%
2017-11-13T11:58:07	mikr	S070	4600000	125000000	12		85077294284886253076854009 2107856332730061202797853001	54	176.905	2.018	1.002	4.036	9.487%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.038	-	-
2001-09-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.076	-	-
2009-11-07T22:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.397	-	-
2016-02-23T16:29:45	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.321	-	-
2013-07-28T11:55:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.489	-	-
2013-10-23T02:43:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.930	-	-
2015-05-18T21:31:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.861	-	-
2016-09-01T17:24:56	kkmrkkblmbrbk	Manual testing	2⁶⁶	2⁶⁷		-	-	3.721	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.621 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:	1.621 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	1.621

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-11-06T17:21:00	sasaki3	ssk_saver	50000	5000000						3	0.540
2012-11-12T21:28:00	Donna Noble	CCI-i7-3770s-XP	50000	5000000						3	0.540
2016-03-12T13:53:53	yooper		50000	5000000						3	0.540

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-28T00:00:00	ANONYMOUS	v4_computers	1FE95D7212CCC3FF	0.501
2015-11-14T18:08:59	MadPoo	Manual testing	1FE95D7212CCC3FF	0.501

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-14T00:00:04

kkmrkkblmbrbk

c4.xlarge

85077294284886253076854009

2107856332730061202797853001

46B7B5A0A11E37__

2018-01-05T08:01:15

ATH

work

85077294284886253076854009

2107856332730061202797853001

46B7B5A0A11E37__

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 = 4600000, B2 = 125000000 (P-1 stage 2)

B1 = 4600000 (P-1 stage 1)

B1 = 225000, B2 = 4556250 (P-1 stage 2)

B1 = 120000, B2 = 2280000 (P-1 stage 2)

B1 = 225000 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 40000, B2 = 610000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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