M447217 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	unknown	3000000	100000000	0.1415	43.3017%	0.1415	43.3017%	43.3017%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	150000	0.0002	18.3434%	0.0002	61.2131%	8.7131%
GPU72	2⁴⁴	0.0000	56.8182%	8000	240000	0.0004	13.6404%	0.0004	62.7083%	5.8902%
Difference	-44	0.0000	-56.8182%	+2992000	+99760000	+0.1411	+29.6613%	+0.1411	-19.4066%	-19.4066%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

3000000

100000000

0.1415

43.3017%

0.1415

43.3017%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

150000

0.0002

18.3434%

0.0002

61.2131%

8.7131%

GPU72

2⁴⁴

0.0000

56.8182%

8000

240000

0.0004

13.6404%

0.0004

62.7083%

5.8902%

Difference

-44

0.0000

-56.8182%

+2992000

+99760000

+0.1411

+29.6613%

+0.1411

-19.4066%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
447217	869389849	9	29.695	972 2² × 3⁵	-	243	243	1.936e-10	4.150e-6	8.446e-6
447217	2576233102022335784317963697	28	91.057	2880294244206208377944 2³ × 11² × 131 × 6966257 × 3260548849	2020-07-08	6966257	3260548849	1.292e+9	3.1462	5.6662

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

447217

869389849

29.695

972
2² × 3⁵

243

1.936e-10

4.150e-6

8.446e-6

447217

2576233102022335784317963697

91.057

2880294244206208377944
2³ × 11² × 131 × 6966257 × 3260548849

2020-07-08

6966257

3260548849

1.292e+9

3.1462

5.6662

exponent	prime factors	composite factor	digits	bits*
447217	869389849 2576233102022335784317963697	2239750907556000102155491026522311753	37	120.753

exponent

prime factors

composite factor

digits

bits*

447217

869389849
2576233102022335784317963697

2239750907556000102155491026522311753

120.753

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T18:48:16	alpertron	Manual testing	3000000	100000000	12	-	skipped known factor: 869389849	-	-	0.141	-	-	34.792%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T18:48:16

alpertron

Manual testing

3000000

100000000

skipped known factor: 869389849

0.141

-

-

34.792%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.112 GHz-days
Estimated T-Level:	26.273

Digits	B1	Curves	Complete	FacMiss
20	11000	444 / 100	4.440	1.154%
25	50000	444 / 280	1.586	20.422%
30	250000	163 / 640	0.255	77.500%

New Calculation Method

Total ECM effort:	14.112 GHz-days
Estimated T-Level:	26.273

Digits	B1	Complete	FacMiss
20	11000	22.648	0.000%
25	50000	2.783	6.185%
30	250000	0.262	76.919%
35	1000000	0.020	98.025%
40	3000000	0.001	99.874%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	3.618
250000	25000000		144	9.270
250000	25000000	2576233102022335784317963697	19	1.223

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-01-02T14:34:00	TJAOI	Manual testing	50000	5000000						50	0.644
2015-04-10T10:22:00	TJAOI	Manual testing	50000	5000000						50	0.644
2016-01-15T14:49:40	TJAOI	Manual testing	50000	5000000						90	1.159
2016-06-03T16:08:38	TJAOI	Manual testing	50000	5000000						91	1.172
2018-07-27T12:38:05	TJAOI	Manual testing	250000	25000000						44	2.833
2020-07-08T10:34:50	nordi	sweet16	250000	25000000	2576233102022335784317963697	91.057	19	2	6197404621907478	19	1.223
2020-07-27T10:56:50	TJAOI	Manual testing	250000	25000000						100	6.438

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-24T17:26:01

Oliver Kruse

Doppelherz

869389849

D2782330412B11__

2017-09-24T17:48:16

Oliver Kruse

Manual testing

869389849

D2782330412B11__

2017-11-07T04:32:13

kkmrkkblmbrbk

c4.xlarge

869389849

D2782330412B11__

2020-04-18T19:04:22

Oliver Kruse

AddPrpType5

869389849

59ECB52F3133C9__

2020-07-08T21:05:39

pew

10980xe_1

869389849

2576233102022335784317963697

59ECB52F3133C9EB

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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