M1465469 Mersenne number exponent details

Residue

Status

L-L

78BE330C0D3ECE7C

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	20.2760	68.6567%	500000	15000000	0.0714	4.9345%	20.3475	70.2033%	1.5466%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9100%	0.0073	63.5913%	1.0913%
GPU72	2⁶⁰	0.1048	65.0000%	6500	100000	0.0006	1.4461%	0.1054	65.5061%	0.5061%
Difference	+7	+20.1712	+3.6567%	+493500	+14900000	+0.0708	+3.4883%	+20.2420	+4.6972%	+4.6972%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.2760

68.6567%

500000

15000000

0.0714

4.9345%

20.3475

70.2033%

1.5466%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9100%

0.0073

63.5913%

1.0913%

GPU72

2⁶⁰

0.1048

65.0000%

6500

100000

0.0006

1.4461%

0.1054

65.5061%

0.5061%

Difference

+20.1712

+3.6567%

+493500

+14900000

+0.0708

+3.4883%

+20.2420

+4.6972%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1465469	247099119337366871	18	57.778	84307180615 5 × 7 × 19387 × 124247	2003-07-30	19387	124247	0.0196	0.0014	0.0022

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1465469

247099119337366871

57.778

84307180615
5 × 7 × 19387 × 124247

2003-07-30

19387

124247

0.0196

0.0014

0.0022

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:14:41	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 247099119337366871	-	-	0.071	-	-	4.934%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-07-30T00:00:00	ANONYMOUS	v4_computers	?	?	247099119337366871	57.778	18	0.006	0.114	0.013
2001-10-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.582 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:	25.582 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
50000	5000000		251	11.90
250000	35000000		50	13.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-23T05:01:55	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2018-09-26T08:49:22	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-04-12T15:23:51	TJAOI	Manual testing	50000	5000000						245	11.62
2022-01-18T14:05:43	TJAOI	Manual testing	250000	35000000						50	13.68

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	78BE330C0D3ECE7C	0.056

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

ANONYMOUS

v4_computers

78BE330C0D3ECE7C

0.056

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T03:53:34

Oliver Kruse

GTX-3

247099119337366871

4EC8B4149AA5A5__

2017-10-28T00:05:04

kkmrkkblmbrbk

c4.xlarge

247099119337366871

4EC8B4149AA5A5__

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)

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