M517043 Mersenne number exponent details

Residue

Status

L-L

E61F969535F804__

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	57.4689	71.6418%	1500000	50000000	0.0876	6.1216%	57.5565	73.3778%	1.7360%
PrimeNet	2⁴⁰	0.0000	52.5000%	5000	180000	0.0003	19.3382%	0.0003	61.6856%	9.1856%
GPU72	2⁴⁴	0.0000	56.8182%	9000	300000	0.0005	14.5804%	0.0005	63.1143%	6.2961%
Difference	+23	+57.4689	+14.8236%	+1491000	+49700000	+0.0871	-8.4587%	+57.5560	+10.2635%	+10.2635%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

57.4689

71.6418%

1500000

50000000

0.0876

6.1216%

57.5565

73.3778%

1.7360%

PrimeNet

2⁴⁰

0.0000

52.5000%

5000

180000

0.0003

19.3382%

0.0003

61.6856%

9.1856%

GPU72

2⁴⁴

0.0000

56.8182%

9000

300000

0.0005

14.5804%

0.0005

63.1143%

6.2961%

Difference

+23

+57.4689

+14.8236%

+1491000

+49700000

+0.0871

-8.4587%

+57.5560

+10.2635%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
517043	5611943249746232479	19	62.283	5426959894773 3 × 54403 × 33251597	2008-01-23	54403	33251597	2.8785	0.0394	0.0715

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

517043

5611943249746232479

62.283

5426959894773
3 × 54403 × 33251597

2008-01-23

54403

33251597

2.8785

0.0394

0.0715

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.510%
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.768%
2002-08-31T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.508%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.376%
2016-03-16T12:43:05	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 5611943249746232479	-	-	0.088	-	-	6.122%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-15T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T07:51:04	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.005	-	-
2001-04-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.019	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.037	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.074	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.071 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	423 / 100	4.230	1.425%
25	50000	423 / 280	1.511	22.016%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.071 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.822	0.000%
25	50000	3.021	4.875%
30	250000	0.287	75.083%
35	1000000	0.022	97.834%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		5611943249746232479	1	0.00000e+0
50000	5000000		279	4.488
250000	25000000		144	11.58

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-18T09:35:00	Chad Davis	Bayes	50000	5000000						1	0.016
2007-09-15T19:51:00	Chad Davis	Bayes	50000	5000000						1	0.016
2008-01-23T08:45:00	James Heinrich	WHS			5611943249746232479	62.283		1		1	-
2015-06-12T09:30:00	TJAOI	Manual testing	50000	5000000						96	1.544
2016-02-26T13:29:41	TJAOI	Manual testing	50000	5000000						90	1.448
2016-09-02T12:15:27	TJAOI	Manual testing	50000	5000000						91	1.464
2018-06-15T13:08:34	TJAOI	Manual testing	250000	25000000						44	3.539
2021-01-01T10:28:34	TJAOI	Manual testing	250000	25000000						100	8.044

date	userid	compid	res64	spent (GHz-days)
2002-04-07T00:00:00	Team Prime Rib	v4_computers	E61F969535F804__	0.008
2002-04-28T00:00:00	Team Prime Rib	v4_computers	E61F969535F804__	0.008

date

userid

compid

res64

spent (GHz-days)

2002-04-07T00:00:00

Team Prime Rib

v4_computers

E61F969535F804__

0.008

2002-04-28T00:00:00

Team Prime Rib

v4_computers

E61F969535F804__

0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T09:52:54

Oliver Kruse

GTX-0

5611943249746232479

55DE66CCCD3F3A__

2017-11-03T03:41:09

kkmrkkblmbrbk

c4.xlarge

5611943249746232479

55DE66CCCD3F3A__

2020-04-19T01:40:36

Oliver Kruse

AddPrpType5

5611943249746232479

71F0C234271522__

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 = 50000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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