M5113709 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	5.8106	65.6716%	-	-	-	-	5.8106	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0601	62.2951%	22000	500000	0.0097	3.4110%	0.0697	63.5812%	1.2861%
GPU72	2⁶⁵	1.4267	64.6154%	34000	700000	0.0141	2.4252%	1.4408	65.4735%	0.8581%
Difference	+2	+4.3839	+1.0563%	-34000	-700000	-0.0141	-2.4252%	+4.3698	+0.1981%	+0.1981%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.8106

65.6716%

5.8106

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0601

62.2951%

22000

500000

0.0097

3.4110%

0.0697

63.5812%

1.2861%

GPU72

2⁶⁵

1.4267

64.6154%

34000

700000

0.0141

2.4252%

1.4408

65.4735%

0.8581%

Difference

+4.3839

+1.0563%

-34000

-700000

-0.0141

-2.4252%

+4.3698

+0.1981%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5113709	116414159920433569	18	56.692	11382556176 2⁴ × 3² × 17 × 19 × 101 × 2423	1998-01-13	101	2423	0.0033	4.573e-5	4.953e-5
5113709	166723332117696132487	21	67.176	16301605362927 3 × 709 × 7664130401	2019-11-12	709	7664130401	7.5149	83.924	156.75

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5113709

116414159920433569

56.692

11382556176
2⁴ × 3² × 17 × 19 × 101 × 2423

1998-01-13

101

2423

0.0033

4.573e-5

4.953e-5

5113709

166723332117696132487

67.176

16301605362927
3 × 709 × 7664130401

2019-11-12

709

7664130401

7.5149

83.924

156.75

exponent	prime factors	composite factor	digits	bits*
5113709	116414159920433569 166723332117696132487	19408956647617035897690062715506256103	38	123.868

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	?	?	116414159920433569	56.692	18	0.001	1.498	0.003
1998-01-26T00:00:00	ANONYMOUS	v4_computers	?	?	116414159920433569	56.692	18	0.001	1.498	0.003
1998-02-19T00:00:00	ANONYMOUS	v4_computers	?	?	116414159920433569	56.692	18	0.001	1.498	0.003

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.422 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.422 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	166723332117696132487	2	0.422

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-11-12T18:43:58	ATH	ec2-ECMCF	50000	5000000	166723332117696132487	67.176	2	2	7287787557576227	2	0.422

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:30:20

kkmrkkblmbrbk

Manual testing

116414159920433569

21C58434F6135F__

2018-05-10T03:33:09

Oliver Kruse

GTX-2

116414159920433569

21C58434F6135F__

2019-11-13T08:09:54

mnd9

221Lb

116414159920433569

166723332117696132487

B734BC9D3177CDF7

2019-11-20T00:19:48

kracker

GRID-11

116414159920433569

166723332117696132487

B734BC9D3177CDF7

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

10¹

10²

10³

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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