M1467097 Mersenne number exponent details

Residue

Status

L-L

8FAEDAFEB3C9D82F

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	20.2535	68.6567%	800000	16000000	0.0901	5.2637%	20.3437	70.3065%	1.6498%
PrimeNet	2⁵⁶	0.0065	62.5000%	7000	120000	0.0007	2.9107%	0.0073	63.5915%	1.0915%
GPU72	2⁶⁰	0.1047	65.0000%	6500	100000	0.0006	1.4465%	0.1053	65.5063%	0.5063%
Difference	+7	+20.1489	+3.6567%	+793500	+15900000	+0.0895	+3.8172%	+20.2384	+4.8003%	+4.8003%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.2535

68.6567%

800000

16000000

0.0901

5.2637%

20.3437

70.3065%

1.6498%

PrimeNet

2⁵⁶

0.0065

62.5000%

7000

120000

0.0007

2.9107%

0.0073

63.5915%

1.0915%

GPU72

2⁶⁰

0.1047

65.0000%

6500

100000

0.0006

1.4465%

0.1053

65.5063%

0.5063%

Difference

+20.1489

+3.6567%

+793500

+15900000

+0.0895

+3.8172%

+20.2384

+4.8003%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1467097	1375579272508022728090583	25	80.186	468809926169852003 11² × 26142029 × 148208167	2009-10-11	26142029	148208167	243,603	1.8155	2.9454

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1467097

1375579272508022728090583

80.186

468809926169852003
11² × 26142029 × 148208167

2009-10-11

26142029

148208167

243,603

1.8155

2.9454

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	20000	265000		-		-	-	0.002	-	-	0.956%
2009-04-25T10:19:00	axn	Manual testing	800000	16000000		-		-	-	0.090	-	-	5.264%
2016-03-17T19:14:43	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.935%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.445 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:	25.445 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
		1375579272508022728090583	1	0.00000e+0
50000	5000000		248	11.76
250000	35000000		50	13.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-07T02:15:00	Steve Scott		50000	5000000						1	0.047
2008-12-24T20:16:00	Never Odd Or Even	G_Quad	50000	5000000						3	0.142
2009-10-11T23:09:00	JimBa	NASsrvr			1375579272508022728090583	80.186		1		1	-
2019-03-29T12:18:12	TJAOI	Manual testing	50000	5000000						244	11.57
2021-12-03T11:50:28	TJAOI	Manual testing	250000	35000000						50	13.68

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T04:10:27

Oliver Kruse

GTX-1

1375579272508022728090583

FB63974B012FCA__

2017-10-28T01:35:36

kkmrkkblmbrbk

c4.xlarge

1375579272508022728090583

FB63974B012FCA__

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 = 800000, B2 = 16000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 800000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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