M1813937 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	16.3809	68.6567%	500000	15000000	0.1015	5.0632%	16.4824	70.2437%	1.5870%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8743%	0.0118	64.2169%	1.0590%
GPU72	2⁶¹	0.1693	65.5738%	9000	130000	0.0012	1.5568%	0.1706	66.1097%	0.5360%
Difference	+6	+16.2116	+3.0829%	+491000	+14870000	+0.1002	+3.5064%	+16.3118	+4.1340%	+4.1340%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3809

68.6567%

500000

15000000

0.1015

5.0632%

16.4824

70.2437%

1.5870%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8743%

0.0118

64.2169%

1.0590%

GPU72

2⁶¹

0.1693

65.5738%

9000

130000

0.0012

1.5568%

0.1706

66.1097%

0.5360%

Difference

+16.2116

+3.0829%

+491000

+14870000

+0.1002

+3.5064%

+16.3118

+4.1340%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1813937	302009626879	12	38.136	83247 3 × 27749	-	3	27749	2.057e-8	0.0001	0.0002
1813937	487228844072936403337	21	68.723	134301479068164 2² × 3 × 11191789922347	2020-06-25	4	11191789922347	62.135	47,965	89,586

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1813937

302009626879

38.136

83247
3 × 27749

27749

2.057e-8

0.0001

0.0002

1813937

487228844072936403337

68.723

134301479068164
2² × 3 × 11191789922347

2020-06-25

11191789922347

62.135

47,965

89,586

exponent	prime factors	composite factor	digits	bits*
1813937	302009626879 487228844072936403337	147147801403153993833703620495223	33	106.859

exponent

prime factors

composite factor

digits

bits*

1813937

302009626879
487228844072936403337

147147801403153993833703620495223

106.859

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 302009626879	-	-	0.101	-	-	5.063%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:17

alpertron

Manual testing

500000

15000000

skipped known factor: 302009626879

0.101

-

-

5.063%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.595 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:	19.595 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.808	0.015%
25	50000	0.798	45.029%
30	250000	0.049	95.184%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	2.553
50000	5000000	487228844072936403337	3	0.207
50000	6500000		218	16.84

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-20T20:59:21	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-01T14:51:08	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-09-29T18:23:40	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-04-30T12:27:22	Greg	azure2	50000	5000000						3	0.207
2020-05-22T22:16:40	Oliver Kruse	IOS-3	50000	5000000						3	0.207
2020-06-25T02:22:27	nordi	sweet16	50000	5000000	487228844072936403337	68.723	3	2	8604382689770426	3	0.207
2020-07-21T20:30:19	-Anonymous-	aws	50000	5000000						3	0.207
2020-09-22T20:22:39	nordi	sweet16	50000	5000000						7	0.483
2020-11-24T15:42:57	nordi	sweet16	50000	5000000						7	0.483
2021-02-21T03:19:49	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2021-03-19T18:34:31	TJAOI	Manual testing	50000	6500000						218	16.84

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T21:38:54

Oliver Kruse

GTX-2

302009626879

6CA5E080CB580B__

2017-11-05T19:56:57

ATH

ec2-1xf

302009626879

6CA5E080CB580B__

2020-06-25T04:17:03

CrypticClue

Manual testing

302009626879

487228844072936403337

B9DCA8C5179CE2E8

2020-06-26T05:10:27

pew

laptop

302009626879

487228844072936403337

B9DCA8C5179CE2E8

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