M1355989 Mersenne number exponent details

Residue

Status

L-L

F222978D9F49AD34

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	21.9131	68.6567%	500000	15000000	0.0714	4.8883%	21.9845	70.1889%	1.5321%
PrimeNet	2⁵⁶	0.0071	62.5000%	6000	100000	0.0006	2.6153%	0.0077	63.4807%	0.9807%
GPU72	2⁶⁰	0.1133	65.0000%	5500	40000	0.0004	0.9826%	0.1137	65.3439%	0.3439%
Difference	+7	+21.7998	+3.6567%	+494500	+14960000	+0.0710	+3.9057%	+21.8708	+4.8450%	+4.8450%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.9131

68.6567%

500000

15000000

0.0714

4.8883%

21.9845

70.1889%

1.5321%

PrimeNet

2⁵⁶

0.0071

62.5000%

6000

100000

0.0006

2.6153%

0.0077

63.4807%

0.9807%

GPU72

2⁶⁰

0.1133

65.0000%

5500

40000

0.0004

0.9826%

0.1137

65.3439%

0.3439%

Difference

+21.7998

+3.6567%

+494500

+14960000

+0.0710

+3.9057%

+21.8708

+4.8450%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1355989	3983532863256053543143	22	71.755	1468866216192039 3³ × 7 × 47 × 165356998333	2009-08-03	47	165356998333	415.09	498.76	931.55

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1355989

3983532863256053543143

71.755

1468866216192039
3³ × 7 × 47 × 165356998333

2009-08-03

165356998333

415.09

498.76

931.55

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.001	-	-	0.798%
2016-03-17T19:05:27	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.888%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-07-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.028	-	-
2022-03-07T17:32:36	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.085	-	-
2009-02-15T06:54:00	Sturle Sunde	gooch.ifi	2⁶⁰	2⁶¹		-	-	0.113	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.082 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.082 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.538	0.000%
25	50000	1.640	19.395%
30	250000	0.140	86.925%
35	1000000	0.010	99.024%

ECM Summary

B1	B2	factor	curves	GHz-days
		3983532863256053543143	1	0.00000e+0
50000	5000000		248	11.61
250000	35000000		50	13.48

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-26T00:01:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-11-24T16:37:00	mognuts	hallowes	50000	5000000						3	0.140
2009-05-03T10:19:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.140
2009-08-03T13:19:00	SubPrime	c2d0			3983532863256053543143	71.755		1		1	-
2018-11-09T13:46:04	TJAOI	Manual testing	50000	5000000						241	11.28
2022-02-10T10:42:32	TJAOI	Manual testing	250000	35000000						50	13.48

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T08:14:19

Oliver Kruse

GTX-1

3983532863256053543143

EB765901EEA7BE__

2017-11-04T18:51:19

kkmrkkblmbrbk

c4.xlarge

3983532863256053543143

EB765901EEA7BE__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (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