M5024183 Mersenne number exponent details

Residue

Status

L-L

A1F7FE90708D5A7B

double-checked

PRP

D54BEFB267128C22

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	2⁷³	380.7274	68.4932%	560000	31360000	0.4498	3.7181%	381.1773	69.6646%	1.1715%
PrimeNet	2⁶¹	0.0611	62.2951%	22000	450000	0.0091	3.3159%	0.0702	63.5453%	1.2503%
GPU72	2⁶⁵	1.4521	64.6154%	34000	700000	0.0141	2.4180%	1.4662	65.4710%	0.8556%
Difference	+8	+379.2753	+3.8778%	+526000	+30660000	+0.4357	+1.3001%	+379.7110	+4.1936%	+4.1936%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

380.7274

68.4932%

560000

31360000

0.4498

3.7181%

381.1773

69.6646%

1.1715%

PrimeNet

2⁶¹

0.0611

62.2951%

22000

450000

0.0091

3.3159%

0.0702

63.5453%

1.2503%

GPU72

2⁶⁵

1.4521

64.6154%

34000

700000

0.0141

2.4180%

1.4662

65.4710%

0.8556%

Difference

+379.2753

+3.8778%

+526000

+30660000

+0.4357

+1.3001%

+379.7110

+4.1936%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5024183	447081225988486008511532197681	30	98.496	44492928102786662877480 2³ × 3 × 5 × 2657 × 4637 × 2085379 × 14430989	2021-10-19	2085379	14430989	2.456e+10	0.5543	0.8530

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5024183

447081225988486008511532197681

98.496

44492928102786662877480
2³ × 3 × 5 × 2657 × 4637 × 2085379 × 14430989

2021-10-19

2085379

14430989

2.456e+10

0.5543

0.8530

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.006%
2009-07-18T12:20:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.006%
2014-11-14T01:20:00	Jocelyn Larouche	Manual testing	67775	67775		-		-	-	0.014	-	-	0.348%
2017-02-14T13:01:44	Squeeky_Squirrel	i5-5250U_1600	300000	9375000	12	-		-	-	0.160	-	-	2.645%
2021-04-04T01:30:55	Dylan Delgado	desktoplinux	560000	31360000		-		-	-	0.450	-	-	3.718%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-10-19T11:43:32	ATH	5960X	2500000	90000000	2	7	447081225988486008511532197681	P-1	30	98.496	1.703

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-10-19T11:43:32

ATH

5960X

2500000

90000000

447081225988486008511532197681

P-1

98.496

1.703

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2016-02-23T16:39:07	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.257	-	-
2014-08-30T01:13:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.391	-	-
2014-09-14T10:24:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.744	-	-
2015-07-27T22:27:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.487	-	-
2016-05-15T21:43:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.975	-	-
2018-06-06T17:06:51	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.949	-	-
2021-02-01T12:43:30	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.90	-	-
2021-04-01T10:41:45	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.80	-	-
2021-04-01T10:41:45	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.60	-	-
2021-04-03T10:35:42	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	95.19	-	-
2021-04-04T19:23:30	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	190.4	-	-

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
2010-06-30T17:49:00	Aca Arsov	backo6400	50000	5000000						3	0.632
2014-05-16T17:22:00	driveByUpgrades	Build_4	50000	5000000						3	0.632
2017-06-21T12:10:02	deo2016	deo2016.home.new	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-28T00:00:00	ANONYMOUS	v4_computers	A1F7FE90708D5A7B	0.696
2000-03-22T00:00:00	ANONYMOUS	v4_computers	A1F7FE90708D5A7B	0.696

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 = 2500000 (P-1 stage 1)

B1 = 560000, B2 = 31360000 (P-1 stage 2)

B1 = 300000, B2 = 9375000 (P-1 stage 2)

B1 = 560000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 67775 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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