M1695899 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	17.5210	68.6567%	500000	15000000	0.0880	5.0223%	17.6091	70.2309%	1.5741%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7300%	0.0123	64.1637%	1.0058%
GPU72	2⁶¹	0.1811	65.5738%	7000	100000	0.0008	1.3006%	0.1820	66.0215%	0.4478%
Difference	+6	+17.3399	+3.0829%	+493000	+14900000	+0.0872	+3.7217%	+17.4271	+4.2093%	+4.2093%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.5210

68.6567%

500000

15000000

0.0880

5.0223%

17.6091

70.2309%

1.5741%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7300%

0.0123

64.1637%

1.0058%

GPU72

2⁶¹

0.1811

65.5738%

7000

100000

0.0008

1.3006%

0.1820

66.0215%

0.4478%

Difference

+17.3399

+3.0829%

+493000

+14900000

+0.0872

+3.7217%

+17.4271

+4.2093%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1695899	1933293808089311	16	50.780	569990845 5 × 719 × 158551	-	719	158551	0.0001	0.0006	0.0011
1695899	115048575269655010201	21	66.641	33919642404900 2² × 3² × 5² × 7² × 19 × 40481731	2018-03-03	49	40481731	12.714	0.1505	0.2811

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1695899

1933293808089311

50.780

569990845
5 × 719 × 158551

719

158551

0.0001

0.0006

0.0011

1695899

115048575269655010201

66.641

33919642404900
2² × 3² × 5² × 7² × 19 × 40481731

2018-03-03

40481731

12.714

0.1505

0.2811

exponent	prime factors	composite factor	digits	bits*
1695899	1933293808089311 115048575269655010201	222422698198321064823678294024061511	36	117.421

exponent

prime factors

composite factor

digits

bits*

1695899

1933293808089311
115048575269655010201

222422698198321064823678294024061511

117.421

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:51	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1933293808089311	-	-	0.088	-	-	5.022%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.451 GHz-days
Estimated T-Level:	24.643

Digits	B1	Curves	Complete	FacMiss
20	11000	260 / 100	2.600	7.331%
25	50000	260 / 280	0.929	39.446%

New Calculation Method

Total ECM effort:	15.451 GHz-days
Estimated T-Level:	24.643

Digits	B1	Complete	FacMiss
20	11000	10.000	0.005%
25	50000	0.925	39.643%
30	250000	0.058	94.331%
35	1000000	0.003	99.728%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	15.27
50000	5000000	115048575269655010201	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-01-14T03:36:16	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-03T16:36:19	ATH	ec2-1xe	50000	5000000	115048575269655010201	66.641	3	2		3	0.178
2019-04-25T09:29:48	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-01-30T15:57:44	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-06T14:10:53	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-14T13:17:05	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-17T11:30:45	TJAOI	Manual testing	50000	5000000						244	14.50

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:23:24

alpertron

Manual testing

1933293808089311

08F3ACFB84EA9B__

2017-10-18T15:29:22

Oliver Kruse

Threadripper

1933293808089311

08F3ACFB84EA9B__

2018-03-08T08:02:03

Oliver Kruse

GTX-3

1933293808089311

115048575269655010201

D48F548E816B64__

2018-03-08T19:24:23

kkmrkkblmbrbk

c5.xlarge

1933293808089311

115048575269655010201

D48F548E816B64__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

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