M2312179 Mersenne number exponent details

Residue

Status

L-L

44EBEA25E198F9CE

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	25.7787	67.6471%	6000000	180000000	1.5164	8.9629%	27.2950	70.5468%	2.8998%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9308%	0.0185	63.1807%	1.1117%
GPU72	2⁶²	0.2657	64.5161%	13000	200000	0.0023	1.7808%	0.2680	65.1480%	0.6319%
Difference	+6	+25.5130	+3.1309%	+5987000	+179800000	+1.5141	+7.1820%	+27.0270	+5.3988%	+5.3988%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.7787

67.6471%

6000000

180000000

1.5164

8.9629%

27.2950

70.5468%

2.8998%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9308%

0.0185

63.1807%

1.1117%

GPU72

2⁶²

0.2657

64.5161%

13000

200000

0.0023

1.7808%

0.2680

65.1480%

0.6319%

Difference

+25.5130

+3.1309%

+5987000

+179800000

+1.5141

+7.1820%

+27.0270

+5.3988%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2312179	25606439871902322271193	23	74.439	5537296176442724 2² × 31 × 39113 × 1141707727	2020-07-30	39113	1141707727	3,282.2	6.0968	11.380

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2312179

25606439871902322271193

74.439

5537296176442724
2² × 31 × 39113 × 1141707727

2020-07-30

39113

1141707727

3,282.2

6.0968

11.380

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.230%
2010-02-15T08:09:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.372%
2018-01-07T05:07:31	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.963%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-14T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.230%

2010-02-15T08:09:00

Bud

annan

500000

10000000

0.100

-

-

4.372%

2018-01-07T05:07:31

Sid & Andy

Hand_In_The_Box

6000000

180000000

1.516

-

-

8.963%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.066	-	-
2009-01-14T22:38:00	Sturle Sunde	dietrich.ifi	2⁶⁰	2⁶¹		-	-	0.066	-	-
2012-05-23T13:44:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.425	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.849	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.616	-	-
2015-10-22T10:17:25	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.232	-	-
2017-05-31T02:32:35	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.464	-	-
2019-04-22T13:11:36	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.93	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.438 GHz-days
Estimated T-Level:	4.200

Digits	B1	Curves	Complete	FacMiss
20	11000	84 / 100	0.840	42.989%
25	50000	84 / 280	0.300	74.042%

New Calculation Method

Total ECM effort:	7.438 GHz-days
Estimated T-Level:	4.200

Digits	B1	Complete	FacMiss
20	11000	2.710	6.656%
25	50000	0.245	78.278%
30	250000	0.015	98.503%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		81	7.173
50000	5000000	25606439871902322271193	3	0.266

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-25T01:34:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.266
2010-01-21T10:17:00	Conductor	home	50000	5000000						3	0.266
2011-11-30T20:17:00	Bud	annan	50000	5000000						3	0.266
2013-10-04T13:54:00	arnaud	srv-630	50000	5000000						3	0.266
2015-06-16T18:26:00	guru	w6	50000	5000000						3	0.266
2016-01-16T09:34:00	Jason U	Server7	50000	5000000						3	0.266
2016-04-27T14:12:07	lettp	Home	50000	5000000						3	0.266
2016-08-11T09:11:21	Bruce	Desk6	50000	5000000						3	0.266
2017-01-16T02:06:00	Bruce	Desk6	50000	5000000						3	0.266
2017-08-30T13:33:55	Bruce	Desk6	50000	5000000						3	0.266
2018-01-28T09:08:50	Bruce	Desk6	50000	5000000						3	0.266
2018-07-23T00:01:12	Bruce	Desk6	50000	5000000						3	0.266
2019-10-23T12:42:24	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.266
2020-03-10T13:19:21	kracker	O0	50000	5000000						3	0.266
2020-03-18T03:30:00	kracker	O0	50000	5000000						3	0.266
2020-03-28T16:13:59	Sergey Nosov	TS140-02	50000	5000000						3	0.266
2020-04-09T10:02:56	mnd9	221Rb	50000	5000000						3	0.266
2020-04-22T07:48:58	mnd9	office2	50000	5000000						3	0.266
2020-04-29T18:29:02	mnd9	fb	50000	5000000						3	0.266
2020-05-11T04:11:16	mnd9	libproj	50000	5000000						3	0.266
2020-05-25T00:43:39	Summy	CHB	50000	5000000						3	0.266
2020-06-13T14:00:01	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.266
2020-06-28T05:41:03	nordi	sweet16	50000	5000000						3	0.266
2020-07-05T12:15:52	mnd9	libproj	50000	5000000						3	0.266
2020-07-11T20:17:31	lycorn	colab_S	50000	5000000						3	0.266
2020-07-24T03:51:52	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.266
2020-07-30T14:29:41	GAN	LMS-06	50000	5000000	25606439871902322271193	74.439	3	2	8787757375034513	3	0.266
2020-08-23T19:40:02	mnd9	75203b	50000	5000000						3	0.266

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	kbutler	v4_computers	44EBEA25E198F9CE	0.156
2018-05-03T19:58:26	kkmrkkblmbrbk	old	44EBEA25E198F9CE	0.156

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

kbutler

v4_computers

44EBEA25E198F9CE

0.156

2018-05-03T19:58:26

kkmrkkblmbrbk

old

44EBEA25E198F9CE

0.156

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 = 6000000, B2 = 180000000 (P-1 stage 2)

B1 = 6000000 (P-1 stage 1)

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

B1 = 500000 (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

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