M1818527 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	16.3396	68.6567%	500000	15000000	0.1015	5.0647%	16.4410	70.2442%	1.5875%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8757%	0.0118	64.2174%	1.0595%
GPU72	2⁶¹	0.1689	65.5738%	9000	130000	0.0012	1.5576%	0.1701	66.1100%	0.5362%
Difference	+6	+16.1706	+3.0829%	+491000	+14870000	+0.1002	+3.5071%	+16.2709	+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

16.3396

68.6567%

500000

15000000

0.1015

5.0647%

16.4410

70.2442%

1.5875%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8757%

0.0118

64.2174%

1.0595%

GPU72

2⁶¹

0.1689

65.5738%

9000

130000

0.0012

1.5576%

0.1701

66.1100%

0.5362%

Difference

+16.1706

+3.0829%

+491000

+14870000

+0.1002

+3.5071%

+16.2709

+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
1818527	87289297	8	26.379	24 2³ × 3	-	8	8	4.942e-12	6.293e-7	1.281e-6
1818527	3556954170493111244743889	25	81.557	977976728003794072 2³ × 103 × 1186864961169653	2020-12-02	103	1186864961169653	454,200	5,086,607	9,500,364

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1818527

87289297

26.379

24
2³ × 3

4.942e-12

6.293e-7

1.281e-6

1818527

3556954170493111244743889

81.557

977976728003794072
2³ × 103 × 1186864961169653

2020-12-02

103

1186864961169653

454,200

5,086,607

9,500,364

exponent	prime factors	composite factor	digits	bits*
1818527	87289297 3556954170493111244743889	310484029003561823896489015856033	33	107.936

exponent

prime factors

composite factor

digits

bits*

1818527

87289297
3556954170493111244743889

310484029003561823896489015856033

107.936

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:45	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 87289297	-	-	0.101	-	-	5.065%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:45

alpertron

Manual testing

500000

15000000

skipped known factor: 87289297

0.101

-

-

5.065%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.710 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:	19.710 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.808	0.015%
25	50000	0.797	45.052%
30	250000	0.049	95.188%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4700000		7	0.472
50000	5000000		26	1.795
50000	5000000	3556954170493111244743889	7	0.483
50000	6600000		218	16.96

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-07-01T08:39:52	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-03T16:06:06	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-10-06T21:55:22	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-02T20:16:34	Greg Hogan	azure	50000	5000000						3	0.207
2020-05-31T22:42:50	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.207
2020-06-29T04:16:40	kracker	O0	50000	5000000						3	0.207
2020-07-26T11:26:55	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-10-04T00:05:34	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2020-12-02T12:55:26	nordi	sweet16	50000	5000000	3556954170493111244743889	81.557	7	2	8315645765883980	7	0.483
2021-03-03T04:12:37	Ducho_YYZ	oracle1	50000	4700000						7	0.472
2021-03-19T18:34:42	TJAOI	Manual testing	50000	6600000						218	16.96

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

10¹⁵

10¹⁶

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