M2054369 Mersenne number exponent details

Residue

Status

L-L

5B351FE90A5F00B3

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	14.4638	68.6567%	270000	4860000	0.0496	3.7931%	14.5134	69.8456%	1.1889%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6667%	0.0203	64.7586%	0.9655%
GPU72	2⁶²	0.2991	66.1290%	9000	120000	0.0014	1.3309%	0.3005	66.5798%	0.4508%
Difference	+5	+14.1647	+2.5277%	+261000	+4740000	+0.0481	+2.4622%	+14.2129	+3.2658%	+3.2658%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.4638

68.6567%

270000

4860000

0.0496

3.7931%

14.5134

69.8456%

1.1889%

PrimeNet

2⁵⁸

0.0187

63.7931%

9000

160000

0.0016

2.6667%

0.0203

64.7586%

0.9655%

GPU72

2⁶²

0.2991

66.1290%

9000

120000

0.0014

1.3309%

0.3005

66.5798%

0.4508%

Difference

+14.1647

+2.5277%

+261000

+4740000

+0.0481

+2.4622%

+14.2129

+3.2658%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2054369	268644800305436143200761	24	77.830	65383774848977020 2² × 5 × 23 × 9059 × 15690323543	2016-05-05	9059	15690323543	19,285	81.500	152.22

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2054369

268644800305436143200761

77.830

65383774848977020
2² × 5 × 23 × 9059 × 15690323543

2016-05-05

9059

15690323543

19,285

81.500

152.22

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.275%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.058%
2009-05-24T19:20:00	Rob_Dee	twopc	20000	280000		-		-	-	0.003	-	-	1.039%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.413%
2011-01-06T01:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.593%
2011-01-21T07:27:00	James Heinrich	i7-920	135000	2902500		-		-	-	0.027	-	-	3.044%
2014-10-26T00:59:00	Jocelyn Larouche	Manual testing	166243	166243		-		-	-	0.016	-	-	1.209%
2016-05-15T21:00:26	Jocelyn Larouche	Manual testing	270000	4860000	6	-		-	-	0.050	-	-	3.793%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:04	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.075	-	-
2009-01-02T09:24:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-03-11T11:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2013-09-01T20:20:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.478	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.956	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.819	-	-
2015-11-03T10:10:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.637	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.726 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	2.726 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.024	35.909%
25	50000	0.092	91.199%
30	250000	0.006	99.433%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	1.782
50000	5000000	268644800305436143200761	3	0.255
50000	6969440		7	0.689

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-09T12:39:00	harlee	P4_2600	50000	5000000						3	0.255
2009-10-24T19:24:00	SubPrime	abd0	50000	5000000						3	0.255
2011-04-15T05:55:00	Scott Crawford	Ecko_2	50000	5000000						3	0.255
2013-03-07T11:13:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-03-31T13:48:00	OS1	L3	50000	5000000						3	0.255
2015-07-12T15:52:00	guru	w1	50000	5000000						3	0.255
2016-02-19T14:34:45	Sintax	cloud	50000	5000000						3	0.255
2016-05-05T13:46:25	Bruce	Desk6	50000	5000000	268644800305436143200761	77.830	3	2		3	0.255
2022-05-14T12:15:22	debrouxl	dl380g9-1	50000	6969440						7	0.689

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	5B351FE90A5F00B3	0.135
1999-03-15T00:00:00	ANONYMOUS	v4_computers	5B351FE90A5F00B3	0.135

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

5B351FE90A5F00B3

0.135

1999-03-15T00:00:00

ANONYMOUS

v4_computers

5B351FE90A5F00B3

0.135

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 = 270000, B2 = 4860000 (P-1 stage 2)

B1 = 135000, B2 = 2902500 (P-1 stage 2)

B1 = 270000 (P-1 stage 1)

B1 = 166243 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 280000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 4000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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