M1819339 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	16.3323	68.6567%	500000	15000000	0.1015	5.0650%	16.4337	70.2443%	1.5875%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8759%	0.0118	64.2175%	1.0596%
GPU72	2⁶¹	0.1688	65.5738%	9000	130000	0.0012	1.5578%	0.1701	66.1100%	0.5363%
Difference	+6	+16.1634	+3.0829%	+491000	+14870000	+0.1002	+3.5072%	+16.2637	+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

16.3323

68.6567%

500000

15000000

0.1015

5.0650%

16.4337

70.2443%

1.5875%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8759%

0.0118

64.2175%

1.0596%

GPU72

2⁶¹

0.1688

65.5738%

9000

130000

0.0012

1.5578%

0.1701

66.1100%

0.5363%

Difference

+16.1634

+3.0829%

+491000

+14870000

+0.1002

+3.5072%

+16.2637

+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
1819339	53379799673865361	17	55.567	14670108120 2³ × 3 × 5 × 47 × 2601083	-	47	2601083	0.0028	0.0112	0.0208
1819339	57658272178110966561697	23	75.610	15845939700658032 2⁴ × 3 × 7 × 1301 × 36249450287	2019-10-07	1301	36249450287	6,347.1	155.36	290.16

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1819339

53379799673865361

55.567

14670108120
2³ × 3 × 5 × 47 × 2601083

2601083

0.0028

0.0112

0.0208

1819339

57658272178110966561697

75.610

15845939700658032
2⁴ × 3 × 7 × 1301 × 36249450287

2019-10-07

1301

36249450287

6,347.1

155.36

290.16

exponent	prime factors	composite factor	digits	bits*
1819339	53379799673865361 57658272178110966561697	3077787018408767990698109739059877677617	40	131.177

exponent

prime factors

composite factor

digits

bits*

1819339

53379799673865361
57658272178110966561697

3077787018408767990698109739059877677617

131.177

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:50	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 53379799673865361	-	-	0.101	-	-	5.065%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:50

alpertron

Manual testing

500000

15000000

skipped known factor: 53379799673865361

0.101

-

-

5.065%

ECM factoring results:

Old Calculation Method

Total ECM effort:

67.608 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	951 / 100	9.510	0.007%
25	50000	951 / 280	3.396	3.329%

New Calculation Method

Total ECM effort:

67.608 GHz-days

Digits	B1	Complete	FacMiss
20	11000	31.176	0.000%
25	50000	2.820	5.963%
30	250000	0.174	84.042%
35	1000000	0.008	99.206%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		726	50.11
50000	5000000	57658272178110966561697	1	0.069
50000	6600000		224	17.43

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-07-04T14:00:58	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-03T21:45:51	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-10-07T21:10:00	Chang Chia-Tche	exbpc13	50000	5000000	57658272178110966561697	75.610	1	2		1	0.069
2020-04-18T11:33:37	Oliver Kruse	IOS-2	50000	5000000						3	0.207
2020-05-07T17:24:06	Greg Hogan	azure	50000	5000000						3	0.207
2020-06-15T15:05:33	nordi	sweet16	50000	5000000						3	0.207
2020-07-12T01:25:21	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-08-14T12:50:58	Ahmed Azhad	c5.large.az	50000	5000000						3	0.207
2020-10-16T20:53:03	nordi	sweet16	50000	5000000						7	0.483
2021-01-01T12:47:51	WoodMan777	Manual testing	50000	5000000						350	24.16
2021-01-02T12:29:55	WoodMan777	Manual testing	50000	5000000						350	24.16
2021-03-26T16:50:03	TJAOI	Manual testing	50000	6600000						224	17.43

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T22:57:45

Oliver Kruse

GTX-3

53379799673865361

1104DA59DEEFF3__

2017-11-06T02:35:17

kkmrkkblmbrbk

old

53379799673865361

1104DA59DEEFF3__

2019-10-08T16:57:27

Daniil Tsarkov

tsar1

53379799673865361

57658272178110966561697

A972FB3C99496A0B

2019-10-09T13:41:13

GAN

GG-AAC

53379799673865361

57658272178110966561697

A972FB3C99496A0B

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