M359837 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	82.5760	71.6418%	131072	13107200	0.0118	3.2060%	82.5878	72.5510%	0.9092%
PrimeNet	2⁴⁰	0.0000	52.5000%	3600	110000	0.0001	16.6749%	0.0001	60.4206%	7.9206%
GPU72	2⁴⁴	0.0000	56.8182%	6500	180000	0.0002	12.3282%	0.0002	62.1417%	5.3235%
Difference	+23	+82.5760	+14.8236%	+124572	+12927200	+0.0116	-9.1222%	+82.5876	+10.4092%	+10.4092%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

82.5760

71.6418%

131072

13107200

0.0118

3.2060%

82.5878

72.5510%

0.9092%

PrimeNet

2⁴⁰

0.0000

52.5000%

3600

110000

0.0001

16.6749%

0.0001

60.4206%

7.9206%

GPU72

2⁴⁴

0.0000

56.8182%

6500

180000

0.0002

12.3282%

0.0002

62.1417%

5.3235%

Difference

+23

+82.5760

+14.8236%

+124572

+12927200

+0.0116

-9.1222%

+82.5876

+10.4092%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
359837	152816271757362487441	21	67.050	212340965155560 2³ × 3² × 5 × 589836014321	2008-01-08	9	589836014321	96.601	451.73	843.71

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

359837

152816271757362487441

67.050

212340965155560
2³ × 3² × 5 × 589836014321

2008-01-08

589836014321

96.601

451.73

843.71

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-10-25T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.001	-	-	1.425%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.003	-	-	1.658%
2002-08-17T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.006	-	-	2.368%
2003-04-03T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.012	-	-	3.206%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	359837	359837		-		-	-	0.005	-	-	1.335%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2001-03-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.027	-	-
2002-02-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.053	-	-
2004-01-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.107	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2001-03-11T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁶

0.027

-

-

2002-02-10T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁷

0.053

-

-

2004-01-27T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.107

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.478 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	424 / 100	4.240	1.410%
25	50000	424 / 280	1.514	21.937%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	10.478 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.860	0.000%
25	50000	3.025	4.858%
30	250000	0.287	75.066%
35	1000000	0.022	97.833%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		152816271757362487441	1	0.00000e+0
50000	5000000		280	2.934
250000	25000000		144	7.545

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-13T03:05:00	ANONYMOUS	Bayes	50000	5000000						1	0.010
2007-08-28T04:41:00	Chad Davis	Bayes	50000	5000000						1	0.010
2007-09-18T03:25:00	Chad Davis	Bayes	50000	5000000						1	0.010
2007-12-16T06:10:00	Steve Scott	Abit	50000	5000000						1	0.010
2007-12-16T08:10:00	Steve Scott	Abit	50000	5000000						1	0.010
2007-12-16T08:16:00	Steve Scott	Abit	50000	5000000						1	0.010
2007-12-16T09:36:00	Sturle Sunde	minister	50000	5000000						1	0.010
2008-01-08T04:45:00	James Heinrich	WHS			152816271757362487441	67.050		1		1	-
2013-12-06T17:29:00	Richard B. Woods	Puttputt	50000	5000000						3	0.031
2013-12-07T19:37:00	Richard B. Woods	Puttputt	50000	5000000						3	0.031
2013-12-08T18:40:00	Richard B. Woods	Puttputt	50000	5000000						3	0.031
2014-10-10T12:42:00	TJAOI	Manual testing	50000	5000000						33	0.346
2015-03-13T11:16:00	TJAOI	Manual testing	50000	5000000						50	0.524
2015-12-18T14:12:57	TJAOI	Manual testing	50000	5000000						90	0.943
2016-07-08T14:13:49	TJAOI	Manual testing	50000	5000000						91	0.954
2018-05-18T10:09:12	TJAOI	Manual testing	250000	25000000						44	2.305
2019-12-09T17:13:42	TJAOI	Manual testing	250000	25000000						100	5.239

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 = 131072, B2 = 13107200 (P-1 stage 2)

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

B1 = 359837 (P-1 stage 1)

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

B1 = 131072 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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