M1729187 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	17.1838	68.6567%	500000	15000000	0.1015	5.0341%	17.2852	70.2346%	1.5778%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7961%	0.0123	64.1880%	1.0302%
GPU72	2⁶¹	0.1776	65.5738%	7000	110000	0.0010	1.3452%	0.1786	66.0369%	0.4631%
Difference	+6	+17.0061	+3.0829%	+493000	+14890000	+0.1005	+3.6889%	+17.1066	+4.1977%	+4.1977%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.1838

68.6567%

500000

15000000

0.1015

5.0341%

17.2852

70.2346%

1.5778%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0012

2.7961%

0.0123

64.1880%

1.0302%

GPU72

2⁶¹

0.1776

65.5738%

7000

110000

0.0010

1.3452%

0.1786

66.0369%

0.4631%

Difference

+17.0061

+3.0829%

+493000

+14890000

+0.1005

+3.6889%

+17.1066

+4.1977%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1729187	968344721	9	29.851	280 2³ × 5 × 7	-	8	8	4.387e-11	6.293e-7	1.281e-6
1729187	210797627289369802250489	24	77.480	60952814036125012 2² × 71 × 450227 × 476698609	2020-05-18	450227	476698609	18,590	2.0765	3.8158
1729187	5182287030294741354674641	25	82.100	1498475014644090360 2³ × 3 × 5 × 23 × 12901571 × 42082141	2019-06-11	12901571	42082141	919,532	1.1399	2.0654

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1729187

968344721

29.851

280
2³ × 5 × 7

4.387e-11

6.293e-7

1.281e-6

1729187

210797627289369802250489

77.480

60952814036125012
2² × 71 × 450227 × 476698609

2020-05-18

450227

476698609

18,590

2.0765

3.8158

1729187

5182287030294741354674641

82.100

1498475014644090360
2³ × 3 × 5 × 23 × 12901571 × 42082141

2019-06-11

12901571

42082141

919,532

1.1399

2.0654

exponent	prime factors	composite factor	digits	bits*
1729187	968344721 210797627289369802250489	204124769584986787426074942818569	33	107.331
1729187	968344721 5182287030294741354674641	5018240288492679864859577284920161	34	111.951
1729187	210797627289369802250489 5182287030294741354674641	1092413809918605961305842883251819107782178149449	49	159.580
1729187	968344721 210797627289369802250489 5182287030294741354674641	10578331459821795223096432224523183466678022289004 88208729	58	189.431

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:32:48	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 968344721	-	-	0.101	-	-	5.034%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:32:48

alpertron

Manual testing

500000

15000000

skipped known factor: 968344721

0.101

-

-

5.034%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.847 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:	17.847 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		193	13.25
50000	5000000	210797627289369802250489	65	4.462
50000	5000000	5182287030294741354674641	2	0.137

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-10-23T16:15:16	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-14T07:17:21	BanWaiLun	na-northeast1-a	50000	5000000						3	0.206
2019-06-12T02:02:25	Chang Chia-Tche	exbpc13	50000	5000000	5182287030294741354674641	82.100	2	2		2	0.137
2020-02-11T06:53:31	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-19T05:10:27	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-27T07:18:08	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-08T15:04:35	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-21T17:38:14	Hans Loeblich	crow	50000	5000000						3	0.206
2020-04-29T13:15:19	Greg	azure2	50000	5000000						3	0.206
2020-05-18T10:40:12	TJAOI	Manual testing	50000	5000000	210797627289369802250489	77.480	65	2		65	4.462
2020-05-18T10:40:12	TJAOI	Manual testing	50000	5000000						168	11.53
2020-05-18T23:00:42	TBB_IL	Small	50000	5000000						3	0.206

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:15:50

alpertron

Manual testing

968344721

A955514C80FDBA__

2017-10-19T07:12:40

Oliver Kruse

Threadripper

968344721

A955514C80FDBA__

2019-06-12T15:14:52

Niels_Mache_Nextcloud

SuperDry-X

968344721

5182287030294741354674641

D5EE0D86F4ECC7C7

2019-06-13T12:59:59

kkmrkkblmbrbk

c5.large

968344721

5182287030294741354674641

D5EE0D86F4ECC7C7

2020-05-18T23:54:03

CrypticClue

cruncher

968344721

210797627289369802250489

5182287030294741354674641

D5EE0D86F4ECC7C7

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

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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