M1747433 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	17.0043	68.6567%	500000	15000000	0.1015	5.0404%	17.1058	70.2366%	1.5798%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8017%	0.0122	64.1901%	1.0322%
GPU72	2⁶¹	0.1758	65.5738%	8000	110000	0.0011	1.4122%	0.1769	66.0599%	0.4862%
Difference	+6	+16.8285	+3.0829%	+492000	+14890000	+0.1004	+3.6282%	+16.9289	+4.1766%	+4.1766%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.0043

68.6567%

500000

15000000

0.1015

5.0404%

17.1058

70.2366%

1.5798%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8017%

0.0122

64.1901%

1.0322%

GPU72

2⁶¹

0.1758

65.5738%

8000

110000

0.0011

1.4122%

0.1769

66.0599%

0.4862%

Difference

+16.8285

+3.0829%

+492000

+14890000

+0.1004

+3.6282%

+16.9289

+4.1766%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1747433	13114093240009	14	43.576	3752388 2² × 3² × 104233	-	9	104233	8.082e-7	0.0004	0.0008
1747433	110774130819472917262084583	27	86.518	31696245526859375227 46523 × 681302700317249	2020-06-01	46523	681302700317249	15,387,785	2,919,893	5,453,547

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1747433

13114093240009

43.576

3752388
2² × 3² × 104233

104233

8.082e-7

0.0004

0.0008

1747433

110774130819472917262084583

86.518

31696245526859375227
46523 × 681302700317249

2020-06-01

46523

681302700317249

15,387,785

2,919,893

5,453,547

exponent	prime factors	composite factor	digits	bits*
1747433	13114093240009 110774130819472917262084583	1452702280147522411807157994483877681247	40	130.094

exponent

prime factors

composite factor

digits

bits*

1747433

13114093240009
110774130819472917262084583

1452702280147522411807157994483877681247

130.094

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:35:11	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 13114093240009	-	-	0.101	-	-	5.040%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:35:11

alpertron

Manual testing

500000

15000000

skipped known factor: 13114093240009

0.101

-

-

5.040%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.867 GHz-days
Estimated T-Level:	24.643

Digits	B1	Curves	Complete	FacMiss
20	11000	260 / 100	2.600	7.331%
25	50000	260 / 280	0.929	39.446%

New Calculation Method

Total ECM effort:	17.867 GHz-days
Estimated T-Level:	24.643

Digits	B1	Complete	FacMiss
20	11000	8.387	0.023%
25	50000	0.758	46.859%
30	250000	0.047	95.439%
35	1000000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.66
50000	5000000	110774130819472917262084583	3	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-03-24T12:29:08	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-18T13:47:13	ATH	ec2-ECMCF	50000	5000000						3	0.206
2019-07-12T11:48:21	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-22T08:26:08	kracker	O0	50000	5000000						3	0.206
2020-03-01T09:59:38	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-13T16:44:16	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-10T03:14:53	Oliver Kruse	Melissa	50000	5000000						3	0.206
2020-05-03T02:27:23	Greg Hogan	azure2	50000	5000000						3	0.206
2020-06-02T03:20:40	Chang Chia-Tche	exbpc13	50000	5000000	110774130819472917262084583	86.518	3	2		3	0.206
2020-06-29T17:16:22	nordi	sweet16	50000	5000000						3	0.206
2020-07-26T12:08:30	MarkS	desktop-i7	50000	5000000						3	0.206
2020-07-27T10:58:45	TJAOI	Manual testing	50000	5000000						229	15.74

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T05:49:21

Oliver Kruse

GTX-2

13114093240009

81C509787B6589__

2017-11-03T19:00:04

srow7

sys2b

13114093240009

81C509787B6589__

2020-06-03T18:08:12

mnd9

50871

13114093240009

110774130819472917262084583

147FDDB69AA06FB0

2020-06-05T01:20:36

Luigi Morelli

9800X

13114093240009

110774130819472917262084583

147FDDB69AA06FB0

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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