M1788439 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	16.6144	68.6567%	500000	15000000	0.1015	5.0546%	16.7159	70.2410%	1.5843%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8140%	0.0119	64.1946%	1.0367%
GPU72	2⁶¹	0.1718	65.5738%	8000	130000	0.0012	1.4931%	0.1729	66.0878%	0.5140%
Difference	+6	+16.4427	+3.0829%	+492000	+14870000	+0.1003	+3.5614%	+16.5430	+4.1532%	+4.1532%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6144

68.6567%

500000

15000000

0.1015

5.0546%

16.7159

70.2410%

1.5843%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8140%

0.0119

64.1946%

1.0367%

GPU72

2⁶¹

0.1718

65.5738%

8000

130000

0.0012

1.4931%

0.1729

66.0878%

0.5140%

Difference

+16.4427

+3.0829%

+492000

+14870000

+0.1003

+3.5614%

+16.5430

+4.1532%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1788439	6308052203705479	16	52.486	1763563701 3 × 587854567	-	3	587854567	0.0006	2.5194	4.7055
1788439	210974398669300422679	21	67.516	58982833261101 3 × 19660944420367	2018-12-11	3	19660944420367	20.163	84,262	157,378
1788439	25375753730064730600117361	26	84.392	7094386146260714120 2³ × 5 × 90749 × 201979 × 9676243	2015-06-23	201979	9676243	3,309,703	0.0565	0.0775

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1788439

6308052203705479

52.486

1763563701
3 × 587854567

587854567

0.0006

2.5194

4.7055

1788439

210974398669300422679

67.516

58982833261101
3 × 19660944420367

2018-12-11

19660944420367

20.163

84,262

157,378

1788439

25375753730064730600117361

84.392

7094386146260714120
2³ × 5 × 90749 × 201979 × 9676243

2015-06-23

201979

9676243

3,309,703

0.0565

0.0775

exponent	prime factors	composite factor	digits	bits*
1788439	6308052203705479 210974398669300422679	1330837520451318807547916504728158241	37	120.002
1788439	6308052203705479 25375753730064730600117361	160071579237622352560404167193636478720919	42	136.878
1788439	210974398669300422679 25375753730064730600117361	5353634383980663736722474027012493044306030119	46	151.907
1788439	6308052203705479 210974398669300422679 25375753730064730600117361	33771005173702650425410708958025672510759576478746 275979322001	62	204.393

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-06-23T20:23:00	alpertron	Manual testing	500000	15000000	12		25375753730064730600117361	26	84.392	0.101	0.194	0.203	5.055%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-06-23T20:23:00

alpertron

Manual testing

500000

15000000

25375753730064730600117361

84.392

0.101

0.194

0.203

5.055%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.774 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.774 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		255	17.57
50000	5000000	210974398669300422679	3	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-14T02:55:11	alpertron	laptop2	50000	5000000						3	0.207
2018-12-11T18:13:29	Chang Chia-Tche	exbpc13	50000	5000000	210974398669300422679	67.516	3	2		3	0.207
2020-03-13T09:30:44	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-09T11:46:41	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-02T20:57:32	Greg Hogan	azure	50000	5000000						3	0.207
2020-06-01T01:54:29	nordi	sweet16	50000	5000000						3	0.207
2020-06-29T09:14:58	argusdusty	Argus-PC	50000	5000000						3	0.207
2020-07-13T17:35:14	argusdusty	Manual testing	50000	5000000						3	0.207
2020-10-05T07:45:33	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.482
2020-11-27T10:33:19	TJAOI	Manual testing	50000	5000000						227	15.64

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T15:44:53

Oliver Kruse

GTX-3

6308052203705479

25375753730064730600117361

DB49B3602E361157

2017-10-05T21:44:06

Oliver Kruse

Manual testing

6308052203705479

25375753730064730600117361

DB49B3602E3611__

2017-11-11T01:52:05

kkmrkkblmbrbk

c4.xlarge

6308052203705479

25375753730064730600117361

DB49B3602E3611__

2018-12-13T17:31:39

oodaira

com1

6308052203705479

210974398669300422679

25375753730064730600117361

3AC5CA8172252B41

2018-12-14T05:57:14

Zero

6308052203705479

210974398669300422679

25375753730064730600117361

3AC5CA8172252B41

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

10¹²

10¹³

10¹⁴

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