M2129807 Mersenne number exponent details

Residue

Status

L-L

9D300E2D41893E52

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	13.9515	67.1642%	2500000	125000000	0.8746	8.5777%	14.8261	69.9807%	2.8166%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	160000	0.0016	2.6849%	0.0197	63.0874%	1.0184%
GPU72	2⁶²	0.2885	64.5161%	10000	150000	0.0017	1.4861%	0.2901	65.0435%	0.5273%
Difference	+5	+13.6630	+2.6481%	+2490000	+124850000	+0.8730	+7.0916%	+14.5360	+4.9373%	+4.9373%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9515

67.1642%

2500000

125000000

0.8746

8.5777%

14.8261

69.9807%

2.8166%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

160000

0.0016

2.6849%

0.0197

63.0874%

1.0184%

GPU72

2⁶²

0.2885

64.5161%

10000

150000

0.0017

1.4861%

0.2901

65.0435%

0.5273%

Difference

+13.6630

+2.6481%

+2490000

+124850000

+0.8730

+7.0916%

+14.5360

+4.9373%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2129807	152460433377681952848786817	27	86.979	35792077258099431744 2⁶ × 3 × 29 × 14723 × 15199 × 28726079	2017-09-21	15199	28726079	12,652,221	0.1506	0.2787

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2129807

152460433377681952848786817

86.979

35792077258099431744
2⁶ × 3 × 29 × 14723 × 15199 × 28726079

2017-09-21

15199

28726079

12,652,221

0.1506

0.2787

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.278%
2009-08-16T00:00:00	harlee	v4_computers	20000	265000		-		-	-	0.003	-	-	1.029%
2010-10-25T21:20:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.775%
2010-11-25T04:35:00	Oscar Östlin		80000	1500000		-		-	-	0.015	-	-	2.376%
2013-11-13T18:49:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.097	-	-	4.775%
2017-09-21T04:28:47	mikr	MSI	2500000	125000000	12		152460433377681952848786817	27	86.979	0.875	0.280	1.749	8.578%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
1999-04-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T19:16:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-13T22:14:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.461	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.922	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.754	-	-
2015-12-27T16:49:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.509	-	-
2016-10-29T15:24:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.017	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.719 GHz-days
Estimated T-Level:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	29 / 280	0.104	90.144%

New Calculation Method

Total ECM effort:	2.719 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	0.936	39.213%
25	50000	0.085	91.892%
30	250000	0.005	99.481%

ECM Summary

B1	B2	factor	curves	GHz-days
40000	6000000		3	0.246
50000	5000000		29	2.472

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-04T12:49:00	Never Odd Or Even	Lap_Dir_2000	50000	5000000						3	0.256
2009-11-26T19:45:00	Conductor	home	50000	5000000						3	0.256
2010-12-29T06:36:00	Oscar Östlin		50000	5000000						2	0.170
2011-01-03T13:48:00	Oscar Östlin		40000	6000000						3	0.246
2013-12-20T13:18:00	arnaud	srv-630	50000	5000000						3	0.256
2015-06-23T16:27:00	nranks	wlaptop	50000	5000000						3	0.256
2016-02-15T17:11:05	Sintax	cloud2	50000	5000000						3	0.256
2016-04-17T09:45:23	Bruce	Desk6	50000	5000000						3	0.256
2016-07-13T15:32:38	Bruce	test	50000	5000000						3	0.256
2016-11-22T08:18:41	NBCC		50000	5000000						3	0.256
2017-06-26T07:54:02	Bruce	Desk6	50000	5000000						3	0.256

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	9D300E2D41893E52	0.140
1999-04-23T00:00:00	ANONYMOUS	v4_computers	9D300E2D41893E52	0.140

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

9D300E2D41893E52

0.140

1999-04-23T00:00:00

ANONYMOUS

v4_computers

9D300E2D41893E52

0.140

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 80000, B2 = 1500000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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