M450301 Mersenne number exponent details

Residue

Status

L-L

4671174E30B63A__

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	65.9868	71.6418%	3000000	100000000	0.1415	7.2014%	66.1283	73.6840%	2.0422%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	150000	0.0002	18.3586%	0.0002	61.2203%	8.7203%
GPU72	2⁴⁴	0.0000	56.8182%	8000	240000	0.0004	13.6524%	0.0004	62.7136%	5.8954%
Difference	+23	+65.9868	+14.8236%	+2992000	+99760000	+0.1411	-6.4510%	+66.1279	+10.9704%	+10.9704%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

65.9868

71.6418%

3000000

100000000

0.1415

7.2014%

66.1283

73.6840%

2.0422%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

150000

0.0002

18.3586%

0.0002

61.2203%

8.7203%

GPU72

2⁴⁴

0.0000

56.8182%

8000

240000

0.0004

13.6524%

0.0004

62.7136%

5.8954%

Difference

+23

+65.9868

+14.8236%

+2992000

+99760000

+0.1411

-6.4510%

+66.1279

+10.9704%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
450301	163099672402852749401	21	67.144	181100721964700 2² × 5² × 1811007219647	2007-09-05	25	1811007219647	102.48	1,685.0	3,147.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

450301

163099672402852749401

67.144

181100721964700
2² × 5² × 1811007219647

2007-09-05

1811007219647

102.48

1,685.0

3,147.2

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.725%
2002-09-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.454%
2016-03-17T18:48:18	alpertron	Manual testing	3000000	100000000	12	-		-	-	0.141	-	-	7.201%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.021	-	-
2002-02-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.043	-	-
2003-12-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.085	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.894 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	12.894 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		163099672402852749401	1	0.00000e+0
50000	5000000		281	3.620
250000	25000000		144	9.274

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-16T09:50:00	drew	messier	50000	5000000						1	0.013
2007-09-05T20:19:00	Chad Davis	Bayes			163099672402852749401	67.144		1		1	-
2013-12-15T04:09:00	Richard B. Woods	Puttputt	50000	5000000						9	0.116
2015-04-24T10:40:00	TJAOI	Manual testing	50000	5000000						90	1.159
2016-01-22T16:32:27	TJAOI	Manual testing	50000	5000000						90	1.159
2016-04-22T16:25:09	TJAOI	Manual testing	50000	5000000						91	1.172
2018-01-05T12:37:47	TJAOI	Manual testing	250000	25000000						44	2.834
2020-09-25T08:51:25	TJAOI	Manual testing	250000	25000000						100	6.440

date	userid	compid	res64	spent (GHz-days)
2002-02-03T00:00:00	ANONYMOUS	v4_computers	4671174E30B63A__	0.005

date

userid

compid

res64

spent (GHz-days)

2002-02-03T00:00:00

ANONYMOUS

v4_computers

4671174E30B63A__

0.005

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-24T21:17:41

Oliver Kruse

Doppelherz

163099672402852749401

AEEA2913A646D5__

2017-09-27T07:33:40

Oliver Kruse

Manual testing

163099672402852749401

AEEA2913A646D5__

2017-11-07T06:31:35

kkmrkkblmbrbk

c4.xlarge

163099672402852749401

AEEA2913A646D5__

2020-04-18T19:34:16

Oliver Kruse

AddPrpType5

163099672402852749401

CC63A3E08E99FB__

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

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

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

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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