M1804133 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	16.4699	68.6567%	500000	15000000	0.1015	5.0599%	16.5714	70.2427%	1.5859%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8714%	0.0119	64.2158%	1.0579%
GPU72	2⁶¹	0.1703	65.5738%	9000	130000	0.0012	1.5551%	0.1715	66.1091%	0.5354%
Difference	+6	+16.2997	+3.0829%	+491000	+14870000	+0.1002	+3.5048%	+16.3999	+4.1335%	+4.1335%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.4699

68.6567%

500000

15000000

0.1015

5.0599%

16.5714

70.2427%

1.5859%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8714%

0.0119

64.2158%

1.0579%

GPU72

2⁶¹

0.1703

65.5738%

9000

130000

0.0012

1.5551%

0.1715

66.1091%

0.5354%

Difference

+16.2997

+3.0829%

+491000

+14870000

+0.1002

+3.5048%

+16.3999

+4.1335%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1804133	25257863	8	24.590	7 7	-	1	7	1.241e-12	1.044e-7	1.601e-7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1804133

25257863

24.590

7
7

1.241e-12

1.044e-7

1.601e-7

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:36:08	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 25257863	-	-	0.101	-	-	5.060%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:36:08

alpertron

Manual testing

500000

15000000

skipped known factor: 25257863

0.101

-

-

5.060%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.791 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:	17.791 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.923	0.005%
25	50000	0.918	39.926%
30	250000	0.058	94.373%
35	1000000	0.003	99.730%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		258	17.79

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-26T12:32:37	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-31T14:43:52	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-09-13T04:42:35	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-04-13T03:39:16	Oliver Kruse	IOS-2	50000	5000000						3	0.207
2020-05-05T01:33:36	Greg Hogan	azure	50000	5000000						3	0.207
2020-06-08T19:59:23	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-07-03T14:40:40	nordi	sweet16	50000	5000000						3	0.207
2020-08-04T19:51:58	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-10-11T05:56:53	nordi	sweet16	50000	5000000						7	0.483
2020-12-11T05:16:07	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.483
2021-01-08T11:40:06	TJAOI	Manual testing	50000	5000000						222	15.31

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

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