M4395029 Mersenne number exponent details

Residue

Status

L-L

91FEB7A09B516660

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	2⁶⁸	13.5619	66.1765%	2237739	62656681	1.0000	7.5696%	14.5619	68.7368%	2.5603%
PrimeNet	2⁶¹	0.0699	62.2951%	18000	360000	0.0066	2.9369%	0.0765	63.4024%	1.1074%
GPU72	2⁶⁵	1.6600	64.6154%	26000	500000	0.0094	2.0314%	1.6694	65.3342%	0.7188%
Difference	+3	+11.9019	+1.5611%	+2211739	+62156681	+0.9906	+5.5382%	+12.8925	+3.4026%	+3.4026%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

13.5619

66.1765%

2237739

62656681

1.0000

7.5696%

14.5619

68.7368%

2.5603%

PrimeNet

2⁶¹

0.0699

62.2951%

18000

360000

0.0066

2.9369%

0.0765

63.4024%

1.1074%

GPU72

2⁶⁵

1.6600

64.6154%

26000

500000

0.0094

2.0314%

1.6694

65.3342%

0.7188%

Difference

+11.9019

+1.5611%

+2211739

+62156681

+0.9906

+5.5382%

+12.8925

+3.4026%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4395029	10915830527318100533977	23	73.209	1241838282218172 2² × 3 × 17 × 6087442559893	2019-07-29	17	6087442559893	560.72	59,980	112,026

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4395029

10915830527318100533977

73.209

1241838282218172
2² × 3 × 17 × 6087442559893

2019-07-29

6087442559893

560.72

59,980

112,026

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-14T05:03:00	Carsten Kossendey	durandal	25000	356250		-		-	-	0.008	-	-	1.198%
2012-01-12T19:52:00	Squeeky_Squirrel	T7500_2200	110000	2255000		-		-	-	0.041	-	-	2.761%
2018-12-03T13:03:46	Ismo Laitela	6600K	2237739	62656681	12	-		-	-	1.000	-	-	7.570%

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		-	-	0.035	-	-
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.070	-	-
2010-11-08T04:27:00	markr	ut	2⁶¹	2⁶²		-	-	0.070	-	-
2012-02-29T05:45:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.363	-	-
2016-02-23T16:38:50	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.223	-	-
2014-08-01T09:52:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.447	-	-
2014-08-01T19:42:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.850	-	-
2015-06-20T11:17:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.700	-	-
2018-05-04T10:56:38	chuenkit	Manual testing	2⁶⁶	2⁶⁷		-	-	3.401	-	-
2018-10-30T00:57:58	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	6.801	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.205 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	2.205 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.462	63.031%
25	50000	0.043	95.819%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.654
50000	5000000	10915830527318100533977	3	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-25T04:30:00	Tydus	TydusCloudEU8	50000	5000000						3	0.551
2013-04-02T09:56:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.551
2016-09-02T07:39:22	bayanne	iMac	50000	5000000						3	0.551
2019-07-29T03:50:58	Corey	Computer	50000	5000000	10915830527318100533977	73.209	3	2		3	0.551

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-05T00:00:00	ANONYMOUS	v4_computers	91FEB7A09B516660	0.548
1999-11-17T00:00:00	cbwood	v4_computers	91FEB7A09B516660	0.548

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-07-29T04:33:43

ATH

ec2-PRPCF

10915830527318100533977

EE4BDA1E65267337

2019-07-30T04:46:20

marssystems

SYSTEM01

10915830527318100533977

EE4BDA1E65267337

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 = 2237739, B2 = 62656681 (P-1 stage 2)

B1 = 2237739 (P-1 stage 1)

B1 = 110000, B2 = 2255000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

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

B1 = 25000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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