M1699877 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	17.4800	68.6567%	500000	15000000	0.0880	5.0237%	17.5681	70.2313%	1.5746%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7313%	0.0123	64.1641%	1.0063%
GPU72	2⁶¹	0.1807	65.5738%	7000	100000	0.0008	1.3013%	0.1815	66.0218%	0.4480%
Difference	+6	+17.2993	+3.0829%	+493000	+14900000	+0.0872	+3.7224%	+17.3865	+4.2096%	+4.2096%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.4800

68.6567%

500000

15000000

0.0880

5.0237%

17.5681

70.2313%

1.5746%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7313%

0.0123

64.1641%

1.0063%

GPU72

2⁶¹

0.1807

65.5738%

7000

100000

0.0008

1.3013%

0.1815

66.0218%

0.4480%

Difference

+17.2993

+3.0829%

+493000

+14900000

+0.0872

+3.7224%

+17.3865

+4.2096%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1699877	1134630500207	13	40.045	333739 7⁴ × 139	-	2401	2401	1.067e-7	0.0002	0.0003
1699877	3244231960086349234351	22	71.458	954254913763275 3⁴ × 5² × 17 × 27719823203	2019-05-02	81	27719823203	490.43	103.06	192.49

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1699877

1134630500207

40.045

333739
7⁴ × 139

2401

1.067e-7

0.0002

0.0003

1699877

3244231960086349234351

71.458

954254913763275
3⁴ × 5² × 17 × 27719823203

2019-05-02

27719823203

490.43

103.06

192.49

exponent	prime factors	composite factor	digits	bits*
1699877	1134630500207 3244231960086349234351	3681004531660310490684166597010657	34	111.504

exponent

prime factors

composite factor

digits

bits*

1699877

1134630500207
3244231960086349234351

3681004531660310490684166597010657

111.504

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:55	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1134630500207	-	-	0.088	-	-	5.024%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:55

alpertron

Manual testing

500000

15000000

skipped known factor: 1134630500207

0.088

-

-

5.024%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.989 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:	15.989 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		268	15.93
50000	5000000	3244231960086349234351	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-12-04T10:53:32	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-05T07:22:29	ATH	ec2-1xe	50000	5000000						3	0.178
2019-05-02T08:52:07	Chang Chia-Tche	exbpc13	50000	5000000	3244231960086349234351	71.458	1	2		1	0.059
2020-01-28T00:43:08	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-03T12:06:46	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-10T23:44:21	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-18T20:35:13	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-27T02:00:22	kracker	O0	50000	5000000						3	0.178
2020-03-07T22:18:56	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-09T11:16:08	TJAOI	Manual testing	50000	5000000						246	14.62

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:16:41

alpertron

Manual testing

1134630500207

7FB40490BC521F__

2017-10-18T17:32:01

Oliver Kruse

Threadripper

1134630500207

7FB40490BC521F__

2019-05-03T09:22:11

artorollo

fourth

1134630500207

3244231960086349234351

20BC174451506331

2019-05-04T06:02:30

kkmrkkblmbrbk

c5.large

1134630500207

3244231960086349234351

20BC174451506331

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

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