M1195429 Mersenne number exponent details

Residue

Status

L-L

EFCD02710DECFE9F

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	24.8563	68.6567%	300000	10000000	0.0368	4.1592%	24.8931	69.9603%	1.3036%
PrimeNet	2⁵⁶	0.0080	62.5000%	5000	80000	0.0004	2.2682%	0.0084	63.3506%	0.8506%
GPU72	2⁶⁰	0.1285	65.0000%	5000	28000	0.0003	0.8022%	0.1288	65.2808%	0.2808%
Difference	+7	+24.7278	+3.6567%	+295000	+9972000	+0.0366	+3.3570%	+24.7644	+4.6796%	+4.6796%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

24.8563

68.6567%

300000

10000000

0.0368

4.1592%

24.8931

69.9603%

1.3036%

PrimeNet

2⁵⁶

0.0080

62.5000%

5000

80000

0.0004

2.2682%

0.0084

63.3506%

0.8506%

GPU72

2⁶⁰

0.1285

65.0000%

5000

28000

0.0003

0.8022%

0.1288

65.2808%

0.2808%

Difference

+24.7278

+3.6567%

+295000

+9972000

+0.0366

+3.3570%

+24.7644

+4.6796%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1195429	322139484229675966361689	24	78.092	134738024688072636 2² × 3 × 227 × 1639607 × 30167777	2008-07-25	1639607	30167777	98,827	0.1420	0.1484
1195429	3189967213798418987964791801	28	91.366	1334235330495754657100 2² × 5² × 13 × 73 × 419 × 20051 × 1673463191	2018-07-27	20051	1673463191	780,894,627	4.0551	7.5722

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1195429

322139484229675966361689

78.092

134738024688072636
2² × 3 × 227 × 1639607 × 30167777

2008-07-25

1639607

30167777

98,827

0.1420

0.1484

1195429

3189967213798418987964791801

91.366

1334235330495754657100
2² × 5² × 13 × 73 × 419 × 20051 × 1673463191

2018-07-27

20051

1673463191

780,894,627

4.0551

7.5722

exponent	prime factors	composite factor	digits	bits*
1195429	322139484229675966361689 3189967213798418987964791801	10276143929625991752900367028666629802215523477118 89	52	169.458

exponent

prime factors

composite factor

digits

bits*

1195429

322139484229675966361689
3189967213798418987964791801

10276143929625991752900367028666629802215523477118
89

169.458

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-05-11T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.005%
2002-09-22T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.049%
2002-09-22T00:00:00	Jocelyn Larouche	v4_computers	5000	5000		-		-	-	0.000	-	-	0.065%
2002-09-29T00:00:00	Jocelyn Larouche	v4_computers	8000	8000		-		-	-	0.000	-	-	0.111%
2002-10-07T00:00:00	Jocelyn Larouche	v4_computers	10000	10000		-		-	-	0.000	-	-	0.140%
2003-09-21T00:00:00	ANONYMOUS	v4_computers	10000	1000000		-		-	-	0.003	-	-	0.991%
unknown			300000	10000000		-		-	-	0.037	-	-	4.159%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.008	-	-
2001-10-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.032	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.353 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.353 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.692	0.000%
25	50000	1.609	20.008%
30	250000	0.131	87.737%
35	1000000	0.009	99.133%

ECM Summary

B1	B2	factor	curves	GHz-days
		322139484229675966361689	1	0.00000e+0
50000	5000000		227	8.366
50000	5000000	3189967213798418987964791801	51	1.880
250000	25000000		44	8.108

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-21T20:49:00	James Heinrich	WHS	50000	5000000						1	0.037
2008-07-25T09:35:00	Team_Bundu	bundu4			322139484229675966361689	78.092		1		1	-
2017-11-17T15:44:05	TJAOI	Manual testing	50000	5000000						136	5.012
2018-07-27T12:42:14	TJAOI	Manual testing	50000	5000000	3189967213798418987964791801	91.366	51	2		51	1.880
2018-07-27T12:42:14	TJAOI	Manual testing	50000	5000000						90	3.317
2020-09-11T10:24:10	TJAOI	Manual testing	250000	25000000						44	8.108

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T12:30:54

Oliver Kruse

GTX-3

322139484229675966361689

7E719D0464E36B__

2017-10-17T20:21:07

Oliver Kruse

Threadripper

322139484229675966361689

7E719D0464E36B__

2018-01-02T21:27:15

ATH

ec2-8x

322139484229675966361689

7E719D0464E36B__

2018-07-28T11:56:08

Gabriel Lignelli

3317U

322139484229675966361689

3189967213798418987964791801

9FC5DDA2A97872__

2018-07-28T16:38:20

Oliver Kruse

GTX-0

322139484229675966361689

3189967213798418987964791801

9FC5DDA2A97872__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 10000, B2 = 1000000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 8000 (P-1 stage 1)

B1 = 5000 (P-1 stage 1)

B1 = 4000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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