M3390061 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	2⁶⁸	17.5822	67.6471%	1050000	111642300	1.0775	7.5144%	18.6598	70.0782%	2.4311%
PrimeNet	2⁶⁰	0.0453	63.3333%	14000	280000	0.0043	2.8457%	0.0496	64.3768%	1.0434%
GPU72	2⁶⁴	1.0499	65.6250%	18000	320000	0.0052	1.7911%	1.0552	66.2407%	0.6157%
Difference	+4	+16.5323	+2.0221%	+1032000	+111322300	+1.0723	+5.7233%	+17.6046	+3.8375%	+3.8375%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.5822

67.6471%

1050000

111642300

1.0775

7.5144%

18.6598

70.0782%

2.4311%

PrimeNet

2⁶⁰

0.0453

63.3333%

14000

280000

0.0043

2.8457%

0.0496

64.3768%

1.0434%

GPU72

2⁶⁴

1.0499

65.6250%

18000

320000

0.0052

1.7911%

1.0552

66.2407%

0.6157%

Difference

+16.5323

+2.0221%

+1032000

+111322300

+1.0723

+5.7233%

+17.6046

+3.8375%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3390061	371469324137	12	38.434	54788 2² × 13697	-	4	13697	2.008e-8	0.0001	0.0002
3390061	1534497551407	13	40.481	226323 3² × 25147	2008-09-30	9	25147	8.588e-8	0.0002	0.0004
3390061	182709547765573625437793	24	77.274	26947825977994736 2⁴ × 21101 × 79817976571	2018-10-22	21101	79817976571	15,587	662.27	1,236.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3390061

371469324137

38.434

54788
2² × 13697

13697

2.008e-8

0.0001

0.0002

3390061

1534497551407

40.481

226323
3² × 25147

2008-09-30

25147

8.588e-8

0.0002

0.0004

3390061

182709547765573625437793

77.274

26947825977994736
2⁴ × 21101 × 79817976571

2018-10-22

21101

79817976571

15,587

662.27

1,236.9

exponent	prime factors	composite factor	digits	bits*
3390061	371469324137 1534497551407	570018768311039703410759	24	78.915
3390061	371469324137 182709547765573625437793	67870992221854553157489756446909641	35	115.708
3390061	1534497551407 182709547765573625437793	280367353664953036285073126898124751	36	117.755
3390061	371469324137 1534497551407 182709547765573625437793	104147871375999354332662151710467636506681414887	48	156.189

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-20T15:08:32	Jocelyn Larouche	Manual testing	339006	3390061	6	-	skipped known factor: 371469324137 skipped known factor: 1534497551407	-	-	0.077	-	-	3.462%
2022-01-07T11:57:35	Jocelyn Larouche	Manual testing	1050000	111642300		-	skipped known factor: 371469324137 skipped known factor: 1534497551407	-	-	1.078	-	-	7.514%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:47:00	markr	Manual testing	?	?	1534497551407	40.481	13	4.26741e-8	0.769	9.21261e-8
2021-08-06T11:21:46	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.817	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.586 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	0.586 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.154	85.740%
25	50000	0.014	98.587%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.440
50000	5000000	182709547765573625437793	1	0.147

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-22T19:34:13	ATH	ec2-ECMCF	50000	5000000	182709547765573625437793	77.274	1	2		1	0.147
2019-08-25T02:37:04	Ivan M	LAB	50000	5000000						3	0.440

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-05T19:04:18

Oliver Kruse

GTX-2

371469324137

1534497551407

DA840C558448BF__

2017-12-15T21:49:51

kkmrkkblmbrbk

c4.xlarge

371469324137

1534497551407

DA840C558448BF__

2018-10-23T17:50:23

trebor

Laptop

371469324137

1534497551407

182709547765573625437793

DA840C558448BF__

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 = 1050000, B2 = 111642300 (P-1 stage 2)

B1 = 1050000 (P-1 stage 1)

B1 = 339006, B2 = 3390061 (P-1 stage 2)

B1 = 339006 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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