M1688773 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	17.5950	68.6567%	500000	15000000	0.0880	5.0197%	17.6830	70.2301%	1.5733%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7279%	0.0124	64.1629%	1.0050%
GPU72	2⁶¹	0.1819	65.5738%	7000	90000	0.0008	1.2568%	0.1827	66.0064%	0.4327%
Difference	+6	+17.4131	+3.0829%	+493000	+14910000	+0.0872	+3.7629%	+17.5003	+4.2236%	+4.2236%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.5950

68.6567%

500000

15000000

0.0880

5.0197%

17.6830

70.2301%

1.5733%

PrimeNet

2⁵⁷

0.0114

63.1579%

8000

130000

0.0010

2.7279%

0.0124

64.1629%

1.0050%

GPU72

2⁶¹

0.1819

65.5738%

7000

90000

0.0008

1.2568%

0.1827

66.0064%

0.4327%

Difference

+17.4131

+3.0829%

+493000

+14910000

+0.0872

+3.7629%

+17.5003

+4.2236%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1688773	445836073	9	28.732	132 2² × 3 × 11	-	4	11	2.178e-11	2.990e-7	5.555e-7
1688773	4873798879	10	32.182	1443 3 × 13 × 37	2008-07-15	13	37	4.446e-10	9.764e-7	1.805e-6
1688773	8228117120050102321513	22	72.801	2436122889236772 2² × 3³ × 431 × 52335715589	2018-02-28	431	52335715589	920.84	194.58	363.42

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1688773

445836073

28.732

132
2² × 3 × 11

2.178e-11

2.990e-7

5.555e-7

1688773

4873798879

32.182

1443
3 × 13 × 37

2008-07-15

4.446e-10

9.764e-7

1.805e-6

1688773

8228117120050102321513

72.801

2436122889236772
2² × 3³ × 431 × 52335715589

2018-02-28

431

52335715589

920.84

194.58

363.42

exponent	prime factors	composite factor	digits	bits*
1688773	445836073 4873798879	2172915352805162167	19	60.914
1688773	445836073 8228117120050102321513	3668391424987207182271539338449	31	101.533
1688773	4873798879 8228117120050102321513	40102187995980897118425356983927	32	104.983
1688773	445836073 4873798879 8228117120050102321513	17879002014835862954295777101337137798671	41	133.715

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:45	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 445836073 skipped known factor: 4873798879	-	-	0.088	-	-	5.020%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:45:00	J Feitsma	Manual testing	?	?	4873798879	32.182	10	1.05822e-10	0.173	2.30308e-10

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:45:00

J Feitsma

Manual testing

4873798879

32.182

1.05822e-10

0.173

2.30308e-10

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.622 GHz-days
Estimated T-Level:	24.696

Digits	B1	Curves	Complete	FacMiss
20	11000	263 / 100	2.630	7.113%
25	50000	263 / 280	0.939	39.025%

New Calculation Method

Total ECM effort:	15.622 GHz-days
Estimated T-Level:	24.696

Digits	B1	Complete	FacMiss
20	11000	8.484	0.021%
25	50000	0.767	46.451%
30	250000	0.047	95.388%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		260	15.44
50000	5000000	8228117120050102321513	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-12-08T21:49:13	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-02-28T15:49:58	Chang Chia-Tche	exbpc13	50000	5000000	8228117120050102321513	72.801	3	2		3	0.178
2019-04-14T10:18:13	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-01-28T04:32:22	kracker	O0	50000	5000000						3	0.178
2020-02-04T09:29:09	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.178
2020-02-11T01:52:27	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-18T23:33:51	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-24T10:24:02	TJAOI	Manual testing	50000	5000000						244	14.49

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T01:29:01

Oliver Kruse

GTX-1

445836073

4873798879

72982953AB2006__

2017-11-03T09:13:50

ATH

ec2-1xf

445836073

4873798879

72982953AB2006__

2018-03-07T08:07:54

Oliver Kruse

GTX-7

445836073

4873798879

8228117120050102321513

C58B40652E6AD8__

2018-03-07T20:40:11

kkmrkkblmbrbk

c5.xlarge

445836073

4873798879

8228117120050102321513

C58B40652E6AD8__

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