M4429589 Mersenne number exponent details

Residue

Status

L-L

2336D83D6EDFAD59

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	2⁷¹	107.9284	67.6056%	10000000	500000000	6.6365	9.0754%	114.5648	70.5455%	2.9399%
PrimeNet	2⁶¹	0.0693	62.2951%	18000	360000	0.0066	2.9409%	0.0760	63.4039%	1.1089%
GPU72	2⁶⁵	1.6470	64.6154%	26000	500000	0.0094	2.0342%	1.6564	65.3352%	0.7198%
Difference	+6	+106.2813	+2.9902%	+9974000	+499500000	+6.6271	+7.0412%	+112.9084	+5.2104%	+5.2104%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

107.9284

67.6056%

10000000

500000000

6.6365

9.0754%

114.5648

70.5455%

2.9399%

PrimeNet

2⁶¹

0.0693

62.2951%

18000

360000

0.0066

2.9409%

0.0760

63.4039%

1.1089%

GPU72

2⁶⁵

1.6470

64.6154%

26000

500000

0.0094

2.0342%

1.6564

65.3352%

0.7198%

Difference

+106.2813

+2.9902%

+9974000

+499500000

+6.6271

+7.0412%

+112.9084

+5.2104%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-20T03:50:00	Carsten Kossendey	durandal	25000	356250		-		-	-	0.008	-	-	0.770%
2012-10-06T18:00:00	Squeeky_Squirrel	P4_2600	290000	7395000		-		-	-	0.122	-	-	3.046%
2021-04-24T06:56:15	Architects Cubed	rdt1	222000	13497000		-		-	-	0.171	-	-	3.281%
2021-08-20T02:36:56	axn	Manual testing	10000000	500000000		-		-	-	6.636	-	-	9.075%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.035	-	-
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.069	-	-
2010-10-21T00:53:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.069	-	-
2012-01-15T23:45:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.360	-	-
2016-02-23T16:38:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.222	-	-
2014-08-30T20:39:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.443	-	-
2014-09-13T18:29:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.844	-	-
2015-06-22T21:38:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.687	-	-
2018-05-17T10:28:52	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.374	-	-
2018-06-26T13:40:12	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	6.748	-	-
2021-06-07T10:34:39	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	13.50	-	-
2021-07-16T16:25:42	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	26.99	-	-
2021-08-09T19:48:15	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	53.98	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.209 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	2.209 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.462	63.031%
25	50000	0.043	95.819%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	2.209

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-31T10:28:00	S00030	vd01	50000	5000000						3	0.552
2013-04-13T05:59:00	Donna Noble	q8200v2	50000	5000000						3	0.552
2016-09-15T06:02:34	bayanne	iMac	50000	5000000						3	0.552
2019-09-30T13:53:17	arnaud	PORTABLE08	50000	5000000						3	0.552

date	userid	compid	res64	spent (GHz-days)
1998-08-30T00:00:00	ANONYMOUS	v4_computers	2336D83D6EDFAD59	0.552
1999-12-15T00:00:00	Bruce A Metcalf	v4_computers	2336D83D6EDFAD59	0.552

date

userid

compid

res64

spent (GHz-days)

1998-08-30T00:00:00

ANONYMOUS

v4_computers

2336D83D6EDFAD59

0.552

1999-12-15T00:00:00

Bruce A Metcalf

v4_computers

2336D83D6EDFAD59

0.552

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 = 10000000, B2 = 500000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 222000, B2 = 13497000 (P-1 stage 2)

B1 = 290000, B2 = 7395000 (P-1 stage 2)

B1 = 290000 (P-1 stage 1)

B1 = 222000 (P-1 stage 1)

B1 = 25000, B2 = 356250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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