M2247379 Mersenne number exponent details

Residue

Status

L-L

706FD7C8FE35E6EB

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	26.5220	67.6471%	1000000	10000000	0.1421	4.6762%	26.6640	69.1600%	1.5129%
PrimeNet	2⁵⁸	0.0171	62.0690%	10000	180000	0.0018	2.8743%	0.0189	63.1592%	1.0903%
GPU72	2⁶²	0.2734	64.5161%	11000	190000	0.0020	1.6596%	0.2753	65.1050%	0.5889%
Difference	+6	+26.2486	+3.1309%	+989000	+9810000	+0.1401	+3.0166%	+26.3887	+4.0549%	+4.0549%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

26.5220

67.6471%

1000000

10000000

0.1421

4.6762%

26.6640

69.1600%

1.5129%

PrimeNet

2⁵⁸

0.0171

62.0690%

10000

180000

0.0018

2.8743%

0.0189

63.1592%

1.0903%

GPU72

2⁶²

0.2734

64.5161%

11000

190000

0.0020

1.6596%

0.2753

65.1050%

0.5889%

Difference

+26.2486

+3.1309%

+989000

+9810000

+0.1401

+3.0166%

+26.3887

+4.0549%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2247379	295469271474349066663467765001	30	97.899	65736413723352640267500 2² × 3 × 5⁴ × 19 × 21521939 × 21434321809	2020-02-20	21521939	21434321809	2.226e+10	113.28	207.94

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2247379

295469271474349066663467765001

97.899

65736413723352640267500
2² × 3 × 5⁴ × 19 × 21521939 × 21434321809

2020-02-20

21521939

21434321809

2.226e+10

113.28

207.94

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-03T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.228%
2010-11-06T12:26:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-11T11:53:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.357%
2011-01-06T15:27:00	markr	tiny	100000	2075000		-		-	-	0.020	-	-	2.403%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	128560	128560		-		-	-	0.012	-	-	0.933%
2015-12-05T15:02:10	Alexander Dubrovin	Manual testing	1000000	10000000	12	-		-	-	0.142	-	-	4.676%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:09	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.051	-	-
2009-01-11T08:41:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-03T19:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.137	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.437	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.874	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.663	-	-
2015-10-27T09:37:30	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.325	-	-
2017-01-08T17:23:37	Conductor	Manual testing	2⁶⁶	2⁶⁷		-	-	6.650	-	-
2019-04-01T13:34:46	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.30	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.606 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	3.606 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.355	25.799%
25	50000	0.122	88.475%
30	250000	0.008	99.249%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.348
50000	5000000	295469271474349066663467765001	3	0.258

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-26T20:57:00	borkencode	CFF2DC1CD	50000	5000000						3	0.258
2009-12-30T01:56:00	SubPrime	stor	50000	5000000						3	0.258
2011-10-21T00:59:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.258
2013-07-12T01:08:00	Kripke	Kripke	50000	5000000						3	0.258
2015-03-28T17:21:00	Jason U	Server7	50000	5000000						3	0.258
2016-02-01T06:03:26	Jason U	Server7	50000	5000000						3	0.258
2016-03-27T20:01:29	Jason U	Server7	50000	5000000						3	0.258
2016-07-16T23:52:35	Bruce	Desk6	50000	5000000						3	0.258
2016-12-03T06:54:28	Bruce	Desk6	50000	5000000						3	0.258
2017-06-27T07:22:10	Bruce	Desk6	50000	5000000						3	0.258
2017-12-10T23:34:17	Bruce	Desk6	50000	5000000						3	0.258
2018-05-14T21:36:24	Bruce	Desk6	50000	5000000						3	0.258
2019-04-05T10:36:20	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-02-20T08:44:31	daveward2005	MW	50000	5000000	295469271474349066663467765001	97.899	3	2		3	0.258

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	706FD7C8FE35E6EB	0.148
2018-04-22T16:56:50	kkmrkkblmbrbk	old	706FD7C8FE35E6EB	0.148

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

706FD7C8FE35E6EB

0.148

2018-04-22T16:56:50

kkmrkkblmbrbk

old

706FD7C8FE35E6EB

0.148

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 = 1000000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 128560 (P-1 stage 1)

B1 = 100000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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