M5559473 Mersenne number exponent details

Residue

Status

L-L

72DDA9DC71823700

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	2⁶⁷	5.3447	65.6716%	50000	5000000	0.0732	3.2214%	5.4179	66.7775%	1.1058%
PrimeNet	2⁶²	0.1105	62.9032%	24000	550000	0.0121	3.1669%	0.1226	64.0781%	1.1748%
GPU72	2⁶⁶	2.6564	65.1515%	34000	700000	0.0161	2.1575%	2.6725	65.9034%	0.7519%
Difference	+1	+2.6883	+0.5201%	+16000	+4300000	+0.0571	+1.0639%	+2.7454	+0.8741%	+0.8741%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.3447

65.6716%

50000

5000000

0.0732

3.2214%

5.4179

66.7775%

1.1058%

PrimeNet

2⁶²

0.1105

62.9032%

24000

550000

0.0121

3.1669%

0.1226

64.0781%

1.1748%

GPU72

2⁶⁶

2.6564

65.1515%

34000

700000

0.0161

2.1575%

2.6725

65.9034%

0.7519%

Difference

+2.6883

+0.5201%

+16000

+4300000

+0.0571

+1.0639%

+2.7454

+0.8741%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5559473	1975988685816809174474328457	28	90.675	177713668707160658436 2² × 3² × 7 × 13 × 23 × 47 × 263 × 190807524437	2015-06-30	263	190807524437	60,682,736	2,380.4	4,445.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5559473

1975988685816809174474328457

90.675

177713668707160658436
2² × 3² × 7 × 13 × 23 × 47 × 263 × 190807524437

2015-06-30

263

190807524437

60,682,736

2,380.4

4,445.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-11-05T00:00:00	ANONYMOUS	v4_computers	20000	20000		-		-	-	0.005	-	-	0.377%
2010-05-04T00:27:00	Squeeky_Squirrel	P4_2600	65000	1121250		-		-	-	0.028	-	-	2.466%
unknown			50000	5000000		-		-	-	0.073	-	-	3.221%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-04-23T19:21:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.177	-	-
2014-12-16T20:34:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.353	-	-
2014-12-17T02:12:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.672	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.720 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.720 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		1975988685816809174474328457	1	0.00000e+0
50000	5000000		3	0.720

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-02-20T20:42:00	alan145	Bear4	50000	5000000						3	0.720
2015-06-30T16:31:00	Sid & Andy	Emperor_Zurg			1975988685816809174474328457	90.675		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	ANONYMOUS	v4_computers	72DDA9DC71823700	0.878
2001-02-04T00:00:00	ANONYMOUS	v4_computers	72DDA9DC71823700	0.878

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T17:00:26

kkmrkkblmbrbk

Manual testing

1975988685816809174474328457

15D537EDDF39D3__

2018-07-07T09:15:47

Battlemaxx

Work-3

1975988685816809174474328457

15D537EDDF39D3__

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 = 50000, B2 = 5000000 (P-1 stage 2)

B1 = 65000, B2 = 1121250 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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