M2423219 Mersenne number exponent details

Residue

Status

L-L

88BFFFF853D91780

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	2⁶⁸	24.5974	67.6471%	1986400	69524000	0.5550	7.1719%	25.1524	69.9674%	2.3203%
PrimeNet	2⁵⁹	0.0317	62.7119%	10000	180000	0.0019	2.5230%	0.0336	63.6527%	0.9408%
GPU72	2⁶³	0.6586	65.0794%	10000	140000	0.0017	1.2774%	0.6603	65.5254%	0.4461%
Difference	+5	+23.9388	+2.5677%	+1976400	+69384000	+0.5533	+5.8945%	+24.4921	+4.4419%	+4.4419%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

24.5974

67.6471%

1986400

69524000

0.5550

7.1719%

25.1524

69.9674%

2.3203%

PrimeNet

2⁵⁹

0.0317

62.7119%

10000

180000

0.0019

2.5230%

0.0336

63.6527%

0.9408%

GPU72

2⁶³

0.6586

65.0794%

10000

140000

0.0017

1.2774%

0.6603

65.5254%

0.4461%

Difference

+23.9388

+2.5677%

+1976400

+69384000

+0.5533

+5.8945%

+24.4921

+4.4419%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2423219	68696706827835685183657	23	75.863	14174679801502812 2² × 3 × 1181223316791901	2020-05-07	4	1181223316791901	5,667.6	6,304,058	11,774,224

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2423219

68696706827835685183657

75.863

14174679801502812
2² × 3 × 1181223316791901

2020-05-07

1181223316791901

5,667.6

6,304,058

11,774,224

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.233%
2010-11-14T17:33:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.203%
2010-11-14T17:54:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.686%
2011-01-24T01:40:00	Oscar Östlin		95000	1923750		-		-	-	0.019	-	-	2.363%
2014-04-17T14:39:00	mikr	MSI	1986400	69524000		-		-	-	0.555	-	-	7.172%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-14T16:02:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-04T23:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.127	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.405	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.810	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.542	-	-
2015-10-23T09:34:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.084	-	-
2017-07-05T06:34:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.168	-	-
2019-04-29T13:20:23	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.34	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.011 GHz-days
Estimated T-Level:	2.250

Digits	B1	Curves	Complete	FacMiss
20	11000	45 / 100	0.450	63.619%
25	50000	45 / 280	0.161	85.129%

New Calculation Method

Total ECM effort:	4.011 GHz-days
Estimated T-Level:	2.250

Digits	B1	Complete	FacMiss
20	11000	1.452	23.419%
25	50000	0.131	87.705%
30	250000	0.008	99.195%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		42	3.744
50000	5000000	68696706827835685183657	3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-04T10:38:00	Martti Järvi	Mardeni	50000	5000000						3	0.267
2010-02-28T03:01:00	James Hintz	ryan	50000	5000000						3	0.267
2012-03-16T19:11:00	S36049	Wolle5	50000	5000000						3	0.267
2013-12-11T23:51:00	Bruce	apandya-DESK11	50000	5000000						3	0.267
2015-07-02T09:58:00	guru	w6	50000	5000000						3	0.267
2016-02-20T06:51:28	Bruce	Desk6	50000	5000000						3	0.267
2016-06-07T12:42:26	Bruce	Desk6	50000	5000000						3	0.267
2016-10-06T02:01:26	Bruce	Desk6	50000	5000000						3	0.267
2017-04-15T09:17:17	Bruce	Desk6	50000	5000000						3	0.267
2017-11-15T22:33:16	Bruce	Desk6	50000	5000000						3	0.267
2018-04-21T12:55:23	Bruce	Desk6	50000	5000000						3	0.267
2019-03-24T18:59:11	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.267
2020-04-19T11:56:16	mnd9	221Rb	50000	5000000						3	0.267
2020-04-28T04:56:09	mnd9	50871b	50000	5000000						3	0.267
2020-05-07T12:56:26	daveward2005	MW	50000	5000000	68696706827835685183657	75.863	3	2		3	0.267

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	MadPoo	v4_computers	88BFFFF853D91780	0.164
2018-05-20T13:59:16	kkmrkkblmbrbk	old	88BFFFF853D91780	0.164

date

userid

compid

res64

spent (GHz-days)

1999-06-15T00:00:00

MadPoo

v4_computers

88BFFFF853D91780

0.164

2018-05-20T13:59:16

kkmrkkblmbrbk

old

88BFFFF853D91780

0.164

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 = 1986400, B2 = 69524000 (P-1 stage 2)

B1 = 1986400 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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