M393541 Mersenne number exponent details

Residue

Status

L-L

20F044748F5D90DA

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	75.5040	71.6418%	100000	10000000	0.0090	2.9030%	75.5130	72.4650%	0.8232%
PrimeNet	2⁴⁰	0.0000	52.5000%	4000	120000	0.0001	17.2667%	0.0001	60.7017%	8.2017%
GPU72	2⁴⁴	0.0000	56.8182%	7000	200000	0.0002	12.8193%	0.0003	62.3538%	5.5356%
Difference	+23	+75.5040	+14.8236%	+93000	+9800000	+0.0087	-9.9163%	+75.5127	+10.1112%	+10.1112%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

75.5040

71.6418%

100000

10000000

0.0090

2.9030%

75.5130

72.4650%

0.8232%

PrimeNet

2⁴⁰

0.0000

52.5000%

4000

120000

0.0001

17.2667%

0.0001

60.7017%

8.2017%

GPU72

2⁴⁴

0.0000

56.8182%

7000

200000

0.0002

12.8193%

0.0003

62.3538%

5.5356%

Difference

+23

+75.5040

+14.8236%

+93000

+9800000

+0.0087

-9.9163%

+75.5127

+10.1112%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
393541	4166405001784478339849	22	71.819	5293482765181364 2² × 13 × 101797745484257	2009-09-05	13	101797745484257	2,425.9	77,963	145,613

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

393541

4166405001784478339849

71.819

5293482765181364
2² × 13 × 101797745484257

2009-09-05

101797745484257

2,425.9

77,963

145,613

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2001-10-13T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.009	-	-	2.903%
2002-06-15T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.003	-	-	1.684%
2002-08-24T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.006	-	-	2.402%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2001-10-13T00:00:00

ANONYMOUS

v4_computers

100000

10000000

0.009

-

-

2.903%

2002-06-15T00:00:00

ANONYMOUS

v4_computers

32768

3276800

0.003

-

-

1.684%

2002-08-24T00:00:00

ANONYMOUS

v4_computers

65536

6553600

0.006

-

-

2.402%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-12-01T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.006	-	-
2022-03-07T06:43:17	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.006	-	-
2001-03-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.024	-	-
2002-01-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.049	-	-
2004-01-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.098	-	-
2008-12-29T02:39:00	Sturle Sunde	gicy.ifi	2⁵⁸	2⁵⁹		-	-	0.098	-	-
2009-01-04T21:08:00	Sturle Sunde	nouchcraft.ifi	2⁵⁹	2⁶⁰		-	-	0.195	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.514 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	423 / 100	4.230	1.425%
25	50000	423 / 280	1.511	22.016%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	10.514 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.822	0.000%
25	50000	3.021	4.875%
30	250000	0.287	75.083%
35	1000000	0.022	97.834%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		4166405001784478339849	1	0.00000e+0
50000	5000000		279	2.936
250000	25000000		144	7.578

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-14T03:04:00	ANONYMOUS	Bayes	50000	5000000						1	0.011
2007-08-30T22:16:00	Chad Davis	Bayes	50000	5000000						1	0.011
2007-10-02T05:52:00	Chad Davis	Bayes	50000	5000000						1	0.011
2008-01-05T15:17:00	Team_Bundu	bundu2	50000	5000000						1	0.011
2008-01-05T16:55:00	Steve Scott	Abit	50000	5000000						1	0.011
2008-01-05T21:24:00	James Heinrich	WHS	50000	5000000						1	0.011
2008-01-06T22:42:00	Team_Bundu	bundu2	50000	5000000						1	0.011
2008-04-05T14:43:00	Scott Kurowski	UW4	50000	5000000						3	0.032
2008-09-16T21:28:00	Sturle Sunde	v21	50000	5000000						3	0.032
2008-11-03T07:15:00	Jayson King	atlas	50000	5000000						3	0.032
2008-12-15T15:43:00	Sturle Sunde	v22	50000	5000000						3	0.032
2009-02-05T20:35:00	Sturle Sunde	v22	50000	5000000						3	0.032
2009-03-08T23:21:00	Sturle Sunde	v22	50000	5000000						3	0.032
2009-04-07T13:46:00	James Hintz	16_060209	50000	5000000						3	0.032
2009-06-04T05:26:00	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.032
2009-07-03T22:13:00	Architects Cubed	m1_50	50000	5000000						3	0.032
2009-07-10T18:22:00	Architects Cubed	m1_70	50000	5000000						3	0.032
2009-07-27T02:30:00	Architects Cubed	m1_44	50000	5000000						3	0.032
2009-09-05T17:36:00	JimBa	NASsrvr			4166405001784478339849	71.819		1		1	-
2014-10-31T13:36:00	TJAOI	Manual testing	50000	5000000						8	0.084
2015-03-20T17:49:00	TJAOI	Manual testing	50000	5000000						50	0.526
2016-01-04T14:28:52	TJAOI	Manual testing	50000	5000000						90	0.947
2016-06-17T16:30:59	TJAOI	Manual testing	50000	5000000						91	0.958
2018-11-02T13:30:24	TJAOI	Manual testing	250000	25000000						44	2.315
2020-03-16T11:24:25	TJAOI	Manual testing	250000	25000000						100	5.262

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 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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