M2062429 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	14.4072	68.6567%	500000	15000000	0.1230	5.1420%	14.5302	70.2684%	1.6117%
PrimeNet	2⁵⁸	0.0186	63.7931%	9000	160000	0.0016	2.6687%	0.0203	64.7593%	0.9662%
GPU72	2⁶²	0.2979	66.1290%	9000	130000	0.0015	1.3653%	0.2994	66.5915%	0.4624%
Difference	+5	+14.1094	+2.5277%	+491000	+14870000	+0.1215	+3.7767%	+14.2309	+3.6769%	+3.6769%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.4072

68.6567%

500000

15000000

0.1230

5.1420%

14.5302

70.2684%

1.6117%

PrimeNet

2⁵⁸

0.0186

63.7931%

9000

160000

0.0016

2.6687%

0.0203

64.7593%

0.9662%

GPU72

2⁶²

0.2979

66.1290%

9000

130000

0.0015

1.3653%

0.2994

66.5915%

0.4624%

Difference

+14.1094

+2.5277%

+491000

+14870000

+0.1215

+3.7767%

+14.2309

+3.6769%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2062429	85041537408721	14	46.273	20616840 2³ × 3² × 5 × 57269	-	9	57269	6.907e-6	0.0003	0.0006
2062429	3930246914944799	16	51.804	952819931 7 × 67 × 2031599	2014-07-11	67	2031599	0.0002	0.0106	0.0197

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2062429

85041537408721

46.273

20616840
2³ × 3² × 5 × 57269

57269

6.907e-6

0.0003

0.0006

2062429

3930246914944799

51.804

952819931
7 × 67 × 2031599

2014-07-11

2031599

0.0002

0.0106

0.0197

exponent	prime factors	composite factor	digits	bits*
2062429	85041537408721 3930246914944799	334234240042788426439216192079	30	98.077

exponent

prime factors

composite factor

digits

bits*

2062429

85041537408721
3930246914944799

334234240042788426439216192079

98.077

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T13:42:51	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 85041537408721 skipped known factor: 3930246914944799	-	-	0.123	-	-	5.142%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-07-11T11:56:00	TJAOI	Manual testing	?	?	3930246914944799	51.804	16	1.16801e-5	0.294	2.52954e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.833 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	2.833 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	1.126	32.449%
25	50000	0.103	90.205%
30	250000	0.006	99.353%

ECM Summary

B1	B2	curves	GHz-days
50000	50000	7	0.355
50000	5000000	6	0.509
50000	5337896	7	0.611
50000	6750000	14	1.358

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-01T18:03:18	Oliver Kruse	ECM-HTC	50000	5000000						3	0.255
2019-07-25T22:21:27	MarkS	laptop64	50000	5000000						3	0.255
2021-08-09T11:19:58	LordJulius	WhiteBox	50000	6750000						7	0.679
2021-11-10T00:47:04	JackBlock		50000	50000						7	0.355
2021-11-25T22:52:20	happy5214	Focus	50000	6750000						7	0.679
2022-05-04T07:33:34	debrouxl	z400	50000	5337896						7	0.611

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T11:21:56

Oliver Kruse

GTX-3

85041537408721

3930246914944799

CEDEB071EBF3CD__

2017-11-16T01:08:54

kkmrkkblmbrbk

c4.xlarge

85041537408721

3930246914944799

CEDEB071EBF3CD__

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