M5064557 Mersenne number exponent details

Residue

Status

L-L

3B6101E7C64764B8

double-checked

PRP

B0DD4CF7B18F8B9A

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	188.8287	68.0556%	1500000	45000000	0.7778	4.9531%	189.6065	69.6378%	1.5822%
PrimeNet	2⁶¹	0.0607	62.2951%	22000	500000	0.0097	3.4056%	0.0703	63.5791%	1.2841%
GPU72	2⁶⁵	1.4405	64.6154%	34000	700000	0.0141	2.4212%	1.4547	65.4721%	0.8567%
Difference	+7	+187.3881	+3.4402%	+1466000	+44300000	+0.7637	+2.5319%	+188.1518	+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

188.8287

68.0556%

1500000

45000000

0.7778

4.9531%

189.6065

69.6378%

1.5822%

PrimeNet

2⁶¹

0.0607

62.2951%

22000

500000

0.0097

3.4056%

0.0703

63.5791%

1.2841%

GPU72

2⁶⁵

1.4405

64.6154%

34000

700000

0.0141

2.4212%

1.4547

65.4721%

0.8567%

Difference

+187.3881

+3.4402%

+1466000

+44300000

+0.7637

+2.5319%

+188.1518

+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
5064557	717407154049889773644623	24	79.247	70826249368887523 7 × 37 × 273460422273697	2021-11-05	37	273460422273697	41,353	2,994,468	5,592,832

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5064557

717407154049889773644623

79.247

70826249368887523
7 × 37 × 273460422273697

2021-11-05

273460422273697

41,353

2,994,468

5,592,832

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-11T00:00:00	ANONYMOUS	v4_computers	20000	20000		-		-	-	0.004	-	-	0.153%
2009-08-11T13:44:00	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	1.236%
2017-07-03T07:50:14	mikr	S061	1500000	45000000	12	-		-	-	0.778	-	-	4.953%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-11-05T11:38:19	ATH	ec2-P_1	2500000	2500000	2	7	717407154049889773644623	P+1	24	79.247	0.844

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-11-05T11:38:19

ATH

ec2-P_1

2500000

717407154049889773644623

P+1

79.247

0.844

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2008-12-29T22:58:00	Sturle Sunde	akerman.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	-	-
2016-05-22T18:45:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.951	-	-
2018-06-11T12:29:31	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.902	-	-
2021-01-25T11:17:47	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.80	-	-
2021-04-01T10:40:39	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.61	-	-
2021-04-01T10:40:39	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.22	-	-
2021-04-03T10:35:13	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.43	-	-

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
2010-07-14T22:08:00	Lukasz Wrobel	4_x_4	50000	5000000						3	0.632
2014-08-12T19:08:00	S36049	Wolle6	50000	5000000						3	0.632
2017-07-12T19:03:13	TwUxTLi51Nus		50000	5000000						3	0.632

date	userid	compid	res64	spent (GHz-days)
1998-07-11T00:00:00	ANONYMOUS	v4_computers	3B6101E7C64764B8	0.702
2000-06-23T00:00:00	ANONYMOUS	v4_computers	3B6101E7C64764B8	0.702

date

userid

compid

res64

spent (GHz-days)

1998-07-11T00:00:00

ANONYMOUS

v4_computers

3B6101E7C64764B8

0.702

2000-06-23T00:00:00

ANONYMOUS

v4_computers

3B6101E7C64764B8

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 = 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 = 20000 (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

10¹⁴

10¹⁵

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