M3360167 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

E91DA65855BC7951

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	17.7387	67.6471%	4000000	150000000	1.8206	8.8014%	19.5592	70.4946%	2.8475%
PrimeNet	2⁶⁰	0.0457	63.3333%	14000	280000	0.0043	2.8412%	0.0500	64.3751%	1.0418%
GPU72	2⁶⁴	1.0593	65.6250%	18000	300000	0.0051	1.7564%	1.0644	66.2288%	0.6038%
Difference	+4	+16.6794	+2.0221%	+3982000	+149700000	+1.8155	+7.0450%	+18.4949	+4.2658%	+4.2658%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.7387

67.6471%

4000000

150000000

1.8206

8.8014%

19.5592

70.4946%

2.8475%

PrimeNet

2⁶⁰

0.0457

63.3333%

14000

280000

0.0043

2.8412%

0.0500

64.3751%

1.0418%

GPU72

2⁶⁴

1.0593

65.6250%

18000

300000

0.0051

1.7564%

1.0644

66.2288%

0.6038%

Difference

+16.6794

+2.0221%

+3982000

+149700000

+1.8155

+7.0450%

+18.4949

+4.2658%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3360167	867561420810479756350632453847	30	99.453	129094985578169144026269 3² × 7 × 67 × 127277 × 2054849 × 116940293	2020-11-19	2054849	116940293	5.288e+10	1.2662	1.8122

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3360167

867561420810479756350632453847

99.453

129094985578169144026269
3² × 7 × 67 × 127277 × 2054849 × 116940293

2020-11-19

2054849

116940293

5.288e+10

1.2662

1.8122

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T04:17:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.810%
2011-10-13T11:33:00	harlee	P4_2600	55000	907500		-		-	-	0.015	-	-	1.830%
2014-06-09T10:16:00	Jocelyn Larouche	Manual testing	76224	76224		-		-	-	0.012	-	-	0.738%
2014-09-29T22:05:00	Jocelyn Larouche	Manual testing	95325	95325		-		-	-	0.015	-	-	0.845%
2015-07-18T01:45:00	Squeeky_Squirrel	P4_2600	230000	6670000		-		-	-	0.088	-	-	3.806%
2020-11-19T04:46:11	mikr	MSI	4000000	150000000	12		867561420810479756350632453847	30	99.453	1.821	0.706	3.641	8.801%
2022-04-08T06:40:59	Jocelyn Larouche	Manual testing	1000000	115661700		-		-	-	1.104	-	-	7.506%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-06-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.046	-	-
2009-03-27T18:50:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-09-07T23:23:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.091	-	-
2012-11-15T00:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.475	-	-
2016-02-23T16:29:26	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.292	-	-
2015-02-11T09:07:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.584	-	-
2015-02-11T09:07:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.112	-	-
2016-03-04T09:43:19	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.224	-	-
2017-03-05T04:56:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.448	-	-
2018-12-03T19:08:40	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.896	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.194 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	2.194 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.194

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-28T20:17:00	Aca Arsov	backo6400	50000	5000000						3	0.439
2011-12-01T13:14:00	Smurgs	Praca	50000	5000000						3	0.439
2014-09-21T17:51:00	Youcef L	breitner	50000	5000000						3	0.439
2016-10-26T17:21:53	Dennis Schreiber	z400	50000	5000000						3	0.439
2019-04-03T07:45:27	furkell	furkell1	50000	5000000						3	0.439

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	AA4D519A674162__	0.353

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

ANONYMOUS

v4_computers

AA4D519A674162__

0.353

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 115661700 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 230000, B2 = 6670000 (P-1 stage 2)

B1 = 230000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 95325 (P-1 stage 1)

B1 = 76224 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (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