M3481319 Mersenne number exponent details

Residue

Status

L-L

BB7615D75B2B9C9F

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	2⁶⁹	34.2936	68.1159%	1000000	114656850	1.0953	6.8995%	35.3889	70.3158%	2.1999%
PrimeNet	2⁶⁰	0.0441	63.3333%	15000	300000	0.0046	2.9577%	0.0488	64.4178%	1.0845%
GPU72	2⁶⁴	1.0224	65.6250%	19000	360000	0.0057	1.8869%	1.0281	66.2736%	0.6486%
Difference	+5	+33.2711	+2.4909%	+981000	+114296850	+1.0896	+5.0126%	+34.3607	+4.0422%	+4.0422%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.2936

68.1159%

1000000

114656850

1.0953

6.8995%

35.3889

70.3158%

2.1999%

PrimeNet

2⁶⁰

0.0441

63.3333%

15000

300000

0.0046

2.9577%

0.0488

64.4178%

1.0845%

GPU72

2⁶⁴

1.0224

65.6250%

19000

360000

0.0057

1.8869%

1.0281

66.2736%

0.6486%

Difference

+33.2711

+2.4909%

+981000

+114296850

+1.0896

+5.0126%

+34.3607

+4.0422%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3481319	870635729137511693071	21	69.561	125043945863265 3⁵ × 5 × 11 × 13 × 317 × 2270341	2012-02-26	317	2270341	64.958	0.0189	0.0352

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3481319

870635729137511693071

69.561

125043945863265
3⁵ × 5 × 11 × 13 × 317 × 2270341

2012-02-26

317

2270341

64.958

0.0189

0.0352

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:46:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.812%
2011-11-13T19:44:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.689%
2021-02-18T11:47:32	Jocelyn Larouche	Manual testing	348131	3829450	6	-	skipped known factor: 870635729137511693071	-	-	0.082	-	-	3.229%
2022-01-22T13:04:49	Jocelyn Larouche	Manual testing	1000000	114656850		-	skipped known factor: 870635729137511693071	-	-	1.095	-	-	6.900%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-19T18:08:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-20T03:34:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.088	-	-
2022-05-27T23:20:16	LordJulius	Manual testing	2¹	2⁶²		-	-	0.176	-	-
2022-05-27T23:20:16	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.282	-	-
2022-05-27T23:20:16	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.564	-	-
2022-05-27T23:20:16	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.073	-	-
2021-02-24T21:45:56	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.147	-	-
2022-05-30T07:59:45	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.147	-	-
2022-05-30T07:59:45	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.293	-	-
2021-06-13T12:36:30	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.586	-	-
2021-12-12T02:00:57	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.17	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.442 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.442 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		870635729137511693071	1	0.00000e+0
50000	5000000		3	0.442

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-15T18:51:00	James Hintz	4115	50000	5000000						3	0.442
2012-02-26T18:51:00	alan145	Bear1			870635729137511693071	69.561		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	dswanson	v4_computers	BB7615D75B2B9C9F	0.366

date

userid

compid

res64

spent (GHz-days)

1999-07-04T00:00:00

dswanson

v4_computers

BB7615D75B2B9C9F

0.366

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-07T09:30:12

Oliver Kruse

GTX-3

870635729137511693071

0E011CDCA18F55__

2017-12-16T21:30:24

kkmrkkblmbrbk

c4.xlarge

870635729137511693071

0E011CDCA18F55__

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 = 1000000, B2 = 114656850 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 348131, B2 = 3829450 (P-1 stage 2)

B1 = 348131 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

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