M1802513 Mersenne number exponent details

Residue

Status

L-L

29352D9E0B5AA54F

double-checked

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	16.4847	68.6567%	500000	15000000	0.1015	5.0593%	16.5862	70.2425%	1.5858%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	150000	0.0012	2.8709%	0.0119	64.2156%	1.0577%
GPU72	2⁶¹	0.1704	65.5738%	9000	130000	0.0012	1.5548%	0.1716	66.1090%	0.5353%
Difference	+6	+16.3143	+3.0829%	+491000	+14870000	+0.1002	+3.5045%	+16.4145	+4.1334%	+4.1334%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.4847

68.6567%

500000

15000000

0.1015

5.0593%

16.5862

70.2425%

1.5858%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

150000

0.0012

2.8709%

0.0119

64.2156%

1.0577%

GPU72

2⁶¹

0.1704

65.5738%

9000

130000

0.0012

1.5548%

0.1716

66.1090%

0.5353%

Difference

+16.3143

+3.0829%

+491000

+14870000

+0.1002

+3.5045%

+16.4145

+4.1334%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1802513	3442623140258922485673877847	28	91.476	954950987942645208571 7 × 22697 × 6010555126496549	2013-07-10	22697	6010555126496549	536,618,707	25,759,737	48,112,014

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1802513

3442623140258922485673877847

91.476

954950987942645208571
7 × 22697 × 6010555126496549

2013-07-10

22697

6010555126496549

536,618,707

25,759,737

48,112,014

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	25000	387500		-		-	-	0.004	-	-	1.198%
2011-02-07T12:28:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.477%
2016-03-16T12:35:57	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.059%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-11T14:32:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.085	-	-
2010-12-13T03:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.885	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.134 GHz-days
Estimated T-Level:	24.696

Digits	B1	Curves	Complete	FacMiss
20	11000	263 / 100	2.630	7.113%
25	50000	263 / 280	0.939	39.025%

New Calculation Method

Total ECM effort:	18.134 GHz-days
Estimated T-Level:	24.696

Digits	B1	Complete	FacMiss
20	11000	8.484	0.021%
25	50000	0.767	46.451%
30	250000	0.047	95.388%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
		3442623140258922485673877847	1	0.00000e+0
50000	5000000		263	18.13

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-09T19:42:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-17T03:53:00	Piepen	T41-2000	50000	5000000						3	0.207
2010-10-12T04:22:00	Lupo	yorick	50000	5000000						3	0.207
2012-03-27T06:59:00	OS1	L3	50000	5000000						3	0.207
2013-07-10T03:01:00	Chang Chia-Tche	exbpc13			3442623140258922485673877847	91.476		1		1	-
2020-06-17T18:10:55	nordi	sweet16	50000	5000000						3	0.207
2020-07-14T11:08:46	kracker	O0	50000	5000000						3	0.207
2020-08-16T08:04:03	MarkS	desktop-i7	50000	5000000						3	0.207
2020-10-18T10:39:17	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.483
2021-01-08T16:38:26	Lisander Viaene		50000	5000000						7	0.483
2021-01-11T22:43:19	Lisander Viaene	Manual testing	50000	5000000						7	0.483
2021-01-29T12:54:54	TJAOI	Manual testing	50000	5000000						221	15.24

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	29352D9E0B5AA54F	0.098

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

29352D9E0B5AA54F

0.098

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)

B1 = 100000, B2 = 1650000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 25000, B2 = 387500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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