M1467281 Mersenne number exponent details

Residue

Status

L-L

D48EFB610B0A0590

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	20.2510	68.6567%	500000	15000000	0.0714	4.9352%	20.3224	70.2036%	1.5469%
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	+20.1463	+3.6567%	+493500	+14900000	+0.0708	+3.4887%	+20.2171	+4.6973%	+4.6973%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.2510

68.6567%

500000

15000000

0.0714

4.9352%

20.3224

70.2036%

1.5469%

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

+20.1463

+3.6567%

+493500

+14900000

+0.0708

+3.4887%

+20.2171

+4.6973%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1467281	10833592694018123028359	23	73.198	3691723907696659 3691723907696659	2019-03-29	1	3691723907696659	1,800.1	11,135,214	20,797,478
1467281	264714545208785593127887	24	77.809	90205811023514103 3² × 61 × 18679 × 19069 × 461297	2009-04-28	19069	461297	40,651	0.0024	0.0026

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1467281

10833592694018123028359

73.198

3691723907696659
3691723907696659

2019-03-29

3691723907696659

1,800.1

11,135,214

20,797,478

1467281

264714545208785593127887

77.809

90205811023514103
3² × 61 × 18679 × 19069 × 461297

2009-04-28

19069

461297

40,651

0.0024

0.0026

exponent	prime factors	composite factor	digits	bits*
1467281	10833592694018123028359 264714545208785593127887	2867809562974229735532591819737785331614747433	46	151.007

exponent

prime factors

composite factor

digits

bits*

1467281

10833592694018123028359
264714545208785593127887

2867809562974229735532591819737785331614747433

151.007

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%
2016-03-17T19:14:43	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 264714545208785593127887	-	-	0.071	-	-	4.935%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.007	-	-
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.007	-	-
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:	25.588 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.588 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
		264714545208785593127887	1	0.00000e+0
50000	5000000		237	11.24
50000	5000000	10833592694018123028359	14	0.664
250000	35000000		50	13.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-07T01:05:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-12-19T16:48:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.142
2009-04-28T15:18:00	axn	Manual testing			264714545208785593127887	77.809		1		1	-
2018-11-25T20:56:45	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-03-29T12:18:13	TJAOI	Manual testing	50000	5000000	10833592694018123028359	73.198	14	2		14	0.664
2019-03-29T12:18:13	TJAOI	Manual testing	50000	5000000						230	10.91
2022-01-18T14:05:57	TJAOI	Manual testing	250000	35000000						50	13.68

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T04:14:43

Oliver Kruse

GTX-1

264714545208785593127887

2B9322AA2904F7__

2017-10-28T01:42:15

kkmrkkblmbrbk

c4.xlarge

264714545208785593127887

2B9322AA2904F7__

2019-03-29T13:35:23

ATH

ec2-PRPCF

10833592694018123028359

264714545208785593127887

6CBEDC2904DFB443

2019-03-30T11:14:03

kkmrkkblmbrbk

c5.large

10833592694018123028359

264714545208785593127887

6CBEDC2904DFB443

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

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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