M2184709 Mersenne number exponent details

Residue

Status

L-L

96C0F9E8F775E4DE

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	13.6009	67.1642%	442971	4429710	0.0629	3.9745%	13.6638	68.4692%	1.3050%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8594%	0.0194	63.1536%	1.0846%
GPU72	2⁶²	0.2812	64.5161%	11000	160000	0.0018	1.5694%	0.2830	65.0730%	0.5569%
Difference	+5	+13.3196	+2.6481%	+431971	+4269710	+0.0611	+2.4051%	+13.3808	+3.3962%	+3.3962%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.6009

67.1642%

442971

4429710

0.0629

3.9745%

13.6638

68.4692%

1.3050%

PrimeNet

2⁵⁸

0.0176

62.0690%

10000

180000

0.0018

2.8594%

0.0194

63.1536%

1.0846%

GPU72

2⁶²

0.2812

64.5161%

11000

160000

0.0018

1.5694%

0.2830

65.0730%

0.5569%

Difference

+13.3196

+2.6481%

+431971

+4269710

+0.0611

+2.4051%

+13.3808

+3.3962%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2184709	11070063681237219190142857	26	83.195	2533532768262779892 2² × 3 × 7 × 397 × 75972555123629	2017-11-03	397	75972555123629	1,597,679	394,620	737,041

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2184709

11070063681237219190142857

83.195

2533532768262779892
2² × 3 × 7 × 397 × 75972555123629

2017-11-03

397

75972555123629

1,597,679

394,620

737,041

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2010-11-06T00:22:00	ANONYMOUS	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-08T11:37:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-13T12:15:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.488%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	119379	119379		-		-	-	0.011	-	-	1.022%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148758	148758		-		-	-	0.014	-	-	1.153%
2016-01-04T02:12:24	Jocelyn Larouche	Manual testing	442971	4429710	6	-		-	-	0.063	-	-	3.974%

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	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-03T01:31:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T11:31:00	Sturle Sunde	corbusier.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-09-15T16:12:00	BloodIce	Manual testing	2⁶²	2⁶³		-	-	0.449	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.899	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.710	-	-
2016-02-08T11:13:48	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.420	-	-
2016-11-24T19:46:06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.841	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.651 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	2.651 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.090	91.358%
30	250000	0.006	99.445%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.566
50000	5000000	11070063681237219190142857	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T10:47:00	mognuts	hallowes	50000	5000000						3	0.257
2010-02-09T06:19:00	James Hintz	ryan	50000	5000000						3	0.257
2011-09-01T02:46:00	Bud	annan	50000	5000000						3	0.257
2013-05-17T00:27:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-05T08:24:00	OS1	L3	50000	5000000						3	0.257
2016-01-30T19:19:53	Bruce	Desk10	50000	5000000						3	0.257
2016-05-07T03:52:47	lettp	Home	50000	5000000						3	0.257
2016-06-25T01:34:34	Jason U	Server7	50000	5000000						3	0.257
2016-10-30T19:20:40	Bruce	Desk6	50000	5000000						3	0.257
2017-04-12T21:38:32	Bruce	Desk6	50000	5000000						3	0.257
2017-11-03T07:44:22	Bruce	Desk6	50000	5000000	11070063681237219190142857	83.195	1	2		1	0.086

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	96C0F9E8F775E4DE	0.144

date

userid

compid

res64

spent (GHz-days)

1999-02-21T00:00:00

ANONYMOUS

v4_computers

96C0F9E8F775E4DE

0.144

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 = 442971, B2 = 4429710 (P-1 stage 2)

B1 = 442971 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148758 (P-1 stage 1)

B1 = 119379 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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