M1455323 Mersenne number exponent details

Residue

Status

L-L

C974D14F83EE7052

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	20.4174	68.6567%	500000	15000000	0.0714	4.9303%	20.4888	70.2020%	1.5453%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9062%	0.0073	63.5898%	1.0898%
GPU72	2⁶⁰	0.1055	65.0000%	6500	90000	0.0006	1.3976%	0.1061	65.4892%	0.4892%
Difference	+7	+20.3119	+3.6567%	+493500	+14910000	+0.0708	+3.5327%	+20.3827	+4.7129%	+4.7129%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.4174

68.6567%

500000

15000000

0.0714

4.9303%

20.4888

70.2020%

1.5453%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9062%

0.0073

63.5898%

1.0898%

GPU72

2⁶⁰

0.1055

65.0000%

6500

90000

0.0006

1.3976%

0.1061

65.4892%

0.4892%

Difference

+20.3119

+3.6567%

+493500

+14910000

+0.0708

+3.5327%

+20.3827

+4.7129%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1455323	46504916485572555953	20	65.334	15977524056712 2³ × 46349 × 43090261	2013-09-01	46349	43090261	7.1381	0.1324	0.2428

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1455323

46504916485572555953

65.334

15977524056712
2³ × 46349 × 43090261

2013-09-01

46349

43090261

7.1381

0.1324

0.2428

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.839%
2010-08-27T10:51:00	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.217%
2010-08-28T13:56:00	Rob_Dee	twopc	200000	300000		-		-	-	0.011	-	-	1.520%
2010-08-29T13:11:00	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.334%
2010-08-30T12:17:00	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.821%
2010-08-31T10:58:00	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	3.112%
2010-09-01T11:19:00	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	3.322%
2010-09-02T11:16:00	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.486%
2016-03-17T19:14:33	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.930%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2010-05-06T19:20:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.106	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.097	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.406 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:	25.406 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.167	0.001%
25	50000	1.348	25.975%
30	250000	0.112	89.363%
35	1000000	0.008	99.239%

ECM Summary

B1	B2	factor	curves	GHz-days
		46504916485572555953	1	0.00000e+0
50000	5000000		248	11.75
250000	35000000		50	13.66

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-05T17:31:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-12-31T19:21:00	Johan Koolwaaij	C0B5A3B75	50000	5000000						3	0.142
2009-09-26T10:15:00	JimBa	NASsrvr	50000	5000000						3	0.142
2010-04-21T16:34:00	Lupo	yorick	50000	5000000						3	0.142
2011-07-22T22:27:00	S36049	Wolle5	50000	5000000						3	0.142
2012-11-23T15:41:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.142
2013-09-01T16:18:00	Chang Chia-Tche	exbpc13			46504916485572555953	65.334		1		1	-
2019-04-12T15:20:42	TJAOI	Manual testing	50000	5000000						232	10.99
2022-01-06T11:54:29	TJAOI	Manual testing	250000	35000000						50	13.66

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	C974D14F83EE7052	0.056

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

C974D14F83EE7052

0.056

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 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 200000, B2 = 4000000 (P-1 stage 2)

B1 = 200000, B2 = 3000000 (P-1 stage 2)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 200000, B2 = 1000000 (P-1 stage 2)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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