M1706591 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	2⁶⁷	17.4113	68.6567%	3000000	273000000	1.2086	9.5075%	18.6198	71.6367%	2.9800%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	130000	0.0010	2.7333%	0.0122	64.1649%	1.0070%
GPU72	2⁶¹	0.1800	65.5738%	7000	100000	0.0008	1.3024%	0.1808	66.0221%	0.4484%
Difference	+6	+17.2313	+3.0829%	+2993000	+272900000	+1.2077	+8.2051%	+18.4390	+5.6145%	+5.6145%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.4113

68.6567%

3000000

273000000

1.2086

9.5075%

18.6198

71.6367%

2.9800%

PrimeNet

2⁵⁷

0.0112

63.1579%

8000

130000

0.0010

2.7333%

0.0122

64.1649%

1.0070%

GPU72

2⁶¹

0.1800

65.5738%

7000

100000

0.0008

1.3024%

0.1808

66.0221%

0.4484%

Difference

+17.2313

+3.0829%

+2993000

+272900000

+1.2077

+8.2051%

+18.4390

+5.6145%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1706591	36705140784353	14	45.061	10753936 2⁴ × 397 × 1693	-	397	1693	4.647e-6	3.191e-5	5.514e-5
1706591	7339958678850925822159	22	72.636	2150473862469369 3 × 2663 × 269179354421	2019-05-11	2663	269179354421	576.03	1,000.8	1,869.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1706591

36705140784353

45.061

10753936
2⁴ × 397 × 1693

397

1693

4.647e-6

3.191e-5

5.514e-5

1706591

7339958678850925822159

72.636

2150473862469369
3 × 2663 × 269179354421

2019-05-11

2663

269179354421

576.03

1,000.8

1,869.2

exponent	prime factors	composite factor	digits	bits*
1706591	36705140784353 7339958678850925822159	269414216658556881064721418647878127	36	117.697

exponent

prime factors

composite factor

digits

bits*

1706591

36705140784353
7339958678850925822159

269414216658556881064721418647878127

117.697

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:29:53	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 36705140784353	-	-	0.088	-	-	5.026%
2021-07-17T07:15:39	Dylan Delgado	laptop-ryzen73700	3000000	273000000		-	skipped known factor: 36705140784353	-	-	1.209	-	-	9.508%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.996 GHz-days
Estimated T-Level:	24.804

Digits	B1	Curves	Complete	FacMiss
20	11000	269 / 100	2.690	6.697%
25	50000	269 / 280	0.961	38.196%

New Calculation Method

Total ECM effort:	15.996 GHz-days
Estimated T-Level:	24.804

Digits	B1	Complete	FacMiss
20	11000	8.677	0.017%
25	50000	0.784	45.646%
30	250000	0.048	95.285%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		267	15.88
50000	5000000	7339958678850925822159	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-06-10T09:02:09	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-08T08:27:44	Oliver Kruse	ECM-HTC	50000	5000000						3	0.178
2019-05-11T14:43:55	Chang Chia-Tche	exbpc13	50000	5000000	7339958678850925822159	72.636	2	2		2	0.119
2020-02-01T16:18:10	kracker	O0	50000	5000000						3	0.178
2020-02-08T21:12:11	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-17T05:10:52	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-25T06:16:05	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-04T21:32:17	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-17T13:48:35	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-30T08:11:43	TJAOI	Manual testing	50000	5000000						245	14.57

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:15:13

alpertron

Manual testing

36705140784353

8BF8FAC873A925__

2017-10-18T20:25:16

Oliver Kruse

Threadripper

36705140784353

8BF8FAC873A925__

2019-05-12T05:06:39

vnatin

SRV1

36705140784353

7339958678850925822159

5039CACAE8EBEBE3

2019-05-13T04:50:39

kkmrkkblmbrbk

c5.large

36705140784353

7339958678850925822159

5039CACAE8EBEBE3

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 = 273000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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