M5073389 Mersenne number exponent details

Residue

Status

L-L

B3C757CD79C7178E

double-checked

PRP

424FA19555CFC535

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	188.5000	68.0556%	1500000	45000000	0.7778	4.9541%	189.2778	69.6381%	1.5826%
PrimeNet	2⁶¹	0.0605	62.2951%	22000	500000	0.0097	3.4065%	0.0702	63.5795%	1.2844%
GPU72	2⁶⁵	1.4380	64.6154%	34000	700000	0.0141	2.4219%	1.4522	65.4724%	0.8570%
Difference	+7	+187.0619	+3.4402%	+1466000	+44300000	+0.7637	+2.5321%	+187.8256	+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

188.5000

68.0556%

1500000

45000000

0.7778

4.9541%

189.2778

69.6381%

1.5826%

PrimeNet

2⁶¹

0.0605

62.2951%

22000

500000

0.0097

3.4065%

0.0702

63.5795%

1.2844%

GPU72

2⁶⁵

1.4380

64.6154%

34000

700000

0.0141

2.4219%

1.4522

65.4724%

0.8570%

Difference

+187.0619

+3.4402%

+1466000

+44300000

+0.7637

+2.5321%

+187.8256

+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
5073389	9312690341947483358421569	25	82.945	917797781911409056 2⁵ × 7 × 42853 × 95613178223	2021-11-06	42853	95613178223	201,250	1,047.0	1,955.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5073389

9312690341947483358421569

82.945

917797781911409056
2⁵ × 7 × 42853 × 95613178223

2021-11-06

42853

95613178223

201,250

1,047.0

1,955.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-15T05:35:00	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	1.237%
2017-07-09T11:09:02	mikr	S063	1500000	45000000	12	-		-	-	0.778	-	-	4.954%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-11-06T09:05:41	ATH	5960X	2500000	87500000	2	7	9312690341947483358421569	P+1	25	82.945	1.676

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-11-06T09:05:41

ATH

5960X

2500000

87500000

9312690341947483358421569

P+1

82.945

1.676

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:08	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.061	-	-
2008-12-28T05:41:00	Sturle Sunde	bakeng.ifi	2⁶¹	2⁶²		-	-	0.061	-	-
2009-08-08T04:06:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.315	-	-
2016-02-23T16:39:08	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.193	-	-
2014-09-01T13:55:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.387	-	-
2014-09-15T10:35:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.736	-	-
2015-08-02T21:34:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.473	-	-
2016-05-23T01:08:41	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.946	-	-
2018-06-11T12:29:32	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.892	-	-
2021-01-18T12:08:09	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.78	-	-
2021-03-31T18:48:12	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.57	-	-
2021-03-31T18:48:13	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.13	-	-
2021-04-02T16:27:58	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.27	-	-

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
2010-07-12T03:26:00	S00030	op9020-usff	50000	5000000						3	0.632
2014-07-13T20:00:00	driveByUpgrades	Build_4	50000	5000000						3	0.632
2017-07-21T07:00:59	driveByUpgrades	AMD8	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-11T00:00:00	ANONYMOUS	v4_computers	B3C757CD79C7178E	0.703
2000-09-15T00:00:00	ANONYMOUS	v4_computers	B3C757CD79C7178E	0.703
2006-02-01T00:00:00	ANONYMOUS	v4_computers	B3C757CD79C7178E	0.703

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 = 87500000 (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)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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