M4605509 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	6.4518	65.6716%	-	-	-	-	6.4518	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0667	62.2951%	19000	400000	0.0076	3.0764%	0.0743	63.4551%	1.1600%
GPU72	2⁶⁵	1.5841	64.6154%	28000	600000	0.0113	2.1875%	1.5954	65.3894%	0.7740%
Difference	+2	+4.8677	+1.0563%	-28000	-600000	-0.0113	-2.1875%	+4.8564	+0.2822%	+0.2822%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.4518

65.6716%

6.4518

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0667

62.2951%

19000

400000

0.0076

3.0764%

0.0743

63.4551%

1.1600%

GPU72

2⁶⁵

1.5841

64.6154%

28000

600000

0.0113

2.1875%

1.5954

65.3894%

0.7740%

Difference

+4.8677

+1.0563%

-28000

-600000

-0.0113

-2.1875%

+4.8564

+0.2822%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4605509	138165271	9	27.042	15 3 × 5	-	3	5	3.895e-12	5.936e-7	1.166e-6
4605509	632524843128281	15	49.168	68670460 2² × 5 × 107 × 32089	2014-04-24	107	32089	2.827e-5	0.0004	0.0006
4605509	1535212112744719337	19	60.413	166671274852 2² × 41667818713	2016-02-05	4	41667818713	0.0506	433.41	809.50
4605509	1722586900053866831657161	25	80.511	187013737249657620 2² × 3 × 5 × 23 × 30137 × 4496705077	2019-04-25	30137	4496705077	69,050	46.779	87.359

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4605509

138165271

27.042

15
3 × 5

3.895e-12

5.936e-7

1.166e-6

4605509

632524843128281

49.168

68670460
2² × 5 × 107 × 32089

2014-04-24

107

32089

2.827e-5

0.0004

0.0006

4605509

1535212112744719337

60.413

166671274852
2² × 41667818713

2016-02-05

41667818713

0.0506

433.41

809.50

4605509

1722586900053866831657161

80.511

187013737249657620
2² × 3 × 5 × 23 × 30137 × 4496705077

2019-04-25

30137

4496705077

69,050

46.779

87.359

exponent	prime factors	composite factor	digits	bits*
4605509	138165271 632524843128281	87392966365051432129151	23	76.210
4605509	138165271 1535212112744719337	212112997599856701015545327	27	87.455
4605509	138165271 1722586900053866831657161	238001685866992425393823028655631	33	107.553
4605509	632524843128281 1535212112744719337	971059800782490442749994432269697	33	109.581
4605509	632524843128281 1722586900053866831657161	1089579008731403979362663282382535270241	40	129.679
4605509	138165271 632524843128281 1535212112744719337	134166740532318804077462965983033831092887	42	136.623
4605509	1535212112744719337 1722586900053866831657161	2644536274218073586528139569892043551222257	43	140.924
4605509	138165271 632524843128281 1722586900053866831657161	150541979017285797019120779692132511279906000311	48	156.721
4605509	138165271 1535212112744719337 1722586900053866831657161	36538307099667045018060235279995763799842551963664 7	51	167.966
4605509	632524843128281 1535212112744719337 1722586900053866831657161	16727348919968357008741270942814686463513418058249 93350217	58	190.092
4605509	138165271 632524843128281 1535212112744719337 1722586900053866831657161	23111386966389853575374870686984166580113630181543 9584805929713807	66	217.134

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-04-24T10:28:00	TJAOI	Manual testing	?	?	632524843128281	49.168	15	1.19838e-5	1.299	2.56716e-5
2016-02-05T12:04:27	TJAOI	Manual testing	2⁶⁰	2⁶¹*	1535212112744719337	60.413	19	0.017	1.232	0.035

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.588 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:	0.588 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1722586900053866831657161	3	0.588

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-04-25T22:48:48	MarkS	laptop64	50000	5000000	1722586900053866831657161	80.511	3	2		3	0.588

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:19:53

kkmrkkblmbrbk

Manual testing

138165271

632524843128281

1535212112744719337

C594180D5EF22405

2018-02-25T17:53:32

ATH

ec2-1xf

138165271

632524843128281

1535212112744719337

C594180D5EF224__

2019-04-26T21:47:39

artorollo

fourth

138165271

632524843128281

1535212112744719337

1722586900053866831657161

799C5A15AC78E70E

2019-04-26T22:35:22

ATH

ec2-PRPCFDC

138165271

632524843128281

1535212112744719337

1722586900053866831657161

799C5A15AC78E70E

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

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