M1819043 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	16.3349	68.6567%	500000	15000000	0.1015	5.0649%	16.4364	70.2442%	1.5875%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8758%	0.0118	64.2174%	1.0595%
GPU72	2⁶¹	0.1689	65.5738%	9000	130000	0.0012	1.5577%	0.1701	66.1100%	0.5363%
Difference	+6	+16.1660	+3.0829%	+491000	+14870000	+0.1002	+3.5072%	+16.2663	+4.1342%	+4.1342%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3349

68.6567%

500000

15000000

0.1015

5.0649%

16.4364

70.2442%

1.5875%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8758%

0.0118

64.2174%

1.0595%

GPU72

2⁶¹

0.1689

65.5738%

9000

130000

0.0012

1.5577%

0.1701

66.1100%

0.5363%

Difference

+16.1660

+3.0829%

+491000

+14870000

+0.1002

+3.5072%

+16.2663

+4.1342%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1819043	3638087	7	21.795	1 1	-	1	1	1.536e-13	7.866e-8	1.601e-7
1819043	582093761	9	29.117	160 2⁵ × 5	2008-07-15	32	32	4.068e-11	2.517e-6	5.123e-6
1819043	5620139361264961119439	22	72.251	1544806626689133 3² × 19 × 71 × 127238829313	2019-10-07	71	127238829313	836.79	545.31	1,018.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1819043

3638087

21.795

1
1

1.536e-13

7.866e-8

1.601e-7

1819043

582093761

29.117

160
2⁵ × 5

2008-07-15

4.068e-11

2.517e-6

5.123e-6

1819043

5620139361264961119439

72.251

1544806626689133
3² × 19 × 71 × 127238829313

2019-10-07

127238829313

836.79

545.31

1,018.5

exponent	prime factors	composite factor	digits	bits*
1819043	3638087 582093761	2117707744675207	16	50.911
1819043	3638087 5620139361264961119439	20446555948406358604136473193	29	94.046
1819043	582093761 5620139361264961119439	3271448058142858935533017720079	31	101.368
1819043	3638087 582093761 5620139361264961119439	11901812651504779236196509838189048873	38	123.163

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:47	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3638087 skipped known factor: 582093761	-	-	0.101	-	-	5.065%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	582093761	29.117	9	1.36166e-12	0.211	2.91506e-12

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:46:00

J Feitsma

Manual testing

582093761

29.117

1.36166e-12

0.211

2.91506e-12

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.624 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.624 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.426	0.022%
25	50000	0.763	46.636%
30	250000	0.047	95.397%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		100	6.902
50000	5000000	5620139361264961119439	3	0.207
50000	6600000		148	11.51

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-07-02T18:06:50	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-03T00:58:41	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-10-07T12:27:01	Chang Chia-Tche	exbpc13	50000	5000000	5620139361264961119439	72.251	3	2		3	0.207
2020-05-03T09:36:20	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-06-03T12:22:11	TBB_IL	Nozomi_Power	50000	5000000						3	0.207
2020-07-02T13:59:46	nordi	sweet16	50000	5000000						3	0.207
2020-07-26T18:47:33	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-10-05T20:22:30	nordi	sweet16	50000	5000000						7	0.483
2020-12-02T21:15:59	MarkS	desktop-i7	50000	5000000						77	5.315
2021-03-19T18:34:55	TJAOI	Manual testing	50000	6600000						148	11.51

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T22:52:15

Oliver Kruse

GTX-1

3638087

582093761

AEB9EE41ED3EBE__

2017-11-06T02:48:50

kkmrkkblmbrbk

old

3638087

582093761

AEB9EE41ED3EBE__

2019-10-08T12:46:33

mnd9

libproj

3638087

582093761

5620139361264961119439

60603CC512414B50

2019-10-12T19:53:30

Chang Chia-Tche

exbpc13

3638087

582093761

5620139361264961119439

60603CC512414B50

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

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