M5066239 Mersenne number exponent details

Residue

Status

L-L

E6154D9B5AAE97C6

double-checked

PRP

AC3C501285D48B5D

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷²	188.7660	68.0556%	1500000	45000000	0.7778	4.9533%	189.5438	69.6379%	1.5823%
PrimeNet	2⁶¹	0.0606	62.2951%	22000	500000	0.0097	3.4057%	0.0703	63.5792%	1.2841%
GPU72	2⁶⁵	1.4401	64.6154%	34000	700000	0.0141	2.4214%	1.4542	65.4722%	0.8568%
Difference	+7	+187.3259	+3.4402%	+1466000	+44300000	+0.7637	+2.5319%	+188.0896	+4.1657%	+4.1657%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

188.7660

68.0556%

1500000

45000000

0.7778

4.9533%

189.5438

69.6379%

1.5823%

PrimeNet

2⁶¹

0.0606

62.2951%

22000

500000

0.0097

3.4057%

0.0703

63.5792%

1.2841%

GPU72

2⁶⁵

1.4401

64.6154%

34000

700000

0.0141

2.4214%

1.4542

65.4722%

0.8568%

Difference

+187.3259

+3.4402%

+1466000

+44300000

+0.7637

+2.5319%

+188.0896

+4.1657%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5066239	1964416473698880012731486921	28	90.666	193873253285018730140 2² × 5 × 617 × 953 × 16485792820507	2021-11-08	953	16485792820507	78,631,790	180,524	337,169

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5066239

1964416473698880012731486921

90.666

193873253285018730140
2² × 5 × 617 × 953 × 16485792820507

2021-11-08

953

16485792820507

78,631,790

180,524

337,169

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-29T00:00:00	ANONYMOUS	v4_computers	25000	281250		-		-	-	0.008	-	-	0.631%
2001-05-20T00:00:00	ANONYMOUS	v4_computers	25000	231250		-		-	-	0.007	-	-	0.591%
2009-08-12T04:27:00	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	1.236%
2017-07-03T10:27:37	mikr	S063	1500000	45000000	12	-		-	-	0.778	-	-	4.953%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-11-08T01:59:27	ATH	ec2-P_1	2500000	90000000	2	7	1964416473698880012731486921	P+1	28	90.666	1.881

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-11-08T01:59:27

ATH

ec2-P_1

2500000

90000000

1964416473698880012731486921

P+1

90.666

1.881

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2008-12-28T20:24:00	Sturle Sunde	antonov.ifi	2⁶¹	2⁶²		-	-	0.061	-	-
2009-08-08T04:05:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.315	-	-
2016-02-23T16:39:08	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.194	-	-
2014-12-14T14:43:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.388	-	-
2014-12-14T14:43:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.738	-	-
2015-08-02T05:19:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.475	-	-
2016-05-22T18:45:47	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.950	-	-
2018-06-11T12:29:31	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.900	-	-
2021-01-25T11:17:43	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.80	-	-
2021-04-01T15:52:17	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.60	-	-
2021-04-01T15:52:17	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.20	-	-
2021-04-03T17:56:48	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 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:	1.897 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	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-09-13T22:03:00	Gerry Snyder	blu	50000	5000000						3	0.632
2014-06-25T04:02:00	S36049	Wolle5	50000	5000000						3	0.632
2017-07-16T04:17:23	bayanne	iMac	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-08-09T00:00:00	ANONYMOUS	v4_computers	EA9CA14938811D__	0.702
2000-07-03T00:00:00	ANONYMOUS	v4_computers	E6154D9B5AAE97C6	0.702
2001-06-17T00:00:00	ANONYMOUS	v4_computers	E6154D9B5AAE97C6	0.702

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 = 2500000, B2 = 90000000 (P+1 stage 2)

B1 = 1500000, B2 = 45000000 (P-1 stage 2)

B1 = 2500000 (P+1 stage 1)

B1 = 1500000 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 25000, B2 = 281250 (P-1 stage 2)

B1 = 25000, B2 = 231250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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