M2137697 Mersenne number exponent details

Residue

Status

L-L

0C46188FF6E46EAE

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	13.9000	67.1642%	500000	15000000	0.1230	5.1642%	14.0230	68.8599%	1.6957%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7308%	0.0197	63.1048%	1.0358%
GPU72	2⁶²	0.2874	64.5161%	10000	150000	0.0017	1.4872%	0.2891	65.0438%	0.5277%
Difference	+5	+13.6126	+2.6481%	+490000	+14850000	+0.1213	+3.6770%	+13.7339	+3.8160%	+3.8160%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9000

67.1642%

500000

15000000

0.1230

5.1642%

14.0230

68.8599%

1.6957%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

170000

0.0017

2.7308%

0.0197

63.1048%

1.0358%

GPU72

2⁶²

0.2874

64.5161%

10000

150000

0.0017

1.4872%

0.2891

65.0438%

0.5277%

Difference

+13.6126

+2.6481%

+490000

+14850000

+0.1213

+3.6770%

+13.7339

+3.8160%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2137697	1136665840891657913	19	59.980	265862243548 2² × 11 × 34213 × 176609	-	34213	176609	0.0417	0.0040	0.0066
2137697	27498139270545223861439	23	74.542	6431720508225727 11 × 13 × 67 × 33757 × 19886231	2022-01-20	33757	19886231	3,140.6	0.1063	0.1929

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2137697

1136665840891657913

59.980

265862243548
2² × 11 × 34213 × 176609

34213

176609

0.0417

0.0040

0.0066

2137697

27498139270545223861439

74.542

6431720508225727
11 × 13 × 67 × 33757 × 19886231

2022-01-20

33757

19886231

3,140.6

0.1063

0.1929

exponent	prime factors	composite factor	digits	bits*
2137697	1136665840891657913 27498139270545223861439	31256195596910207611808301224168499916807	41	134.521

exponent

prime factors

composite factor

digits

bits*

2137697

1136665840891657913
27498139270545223861439

31256195596910207611808301224168499916807

134.521

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.278%
2016-03-26T11:55:00	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1136665840891657913	-	-	0.123	-	-	5.164%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.365 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.365 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.499	60.687%
25	50000	0.045	95.554%
30	250000	0.003	99.720%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.512
50000	5000000	27498139270545223861439	2	0.171
50000	6750000		7	0.683

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-09T00:21:15	limurchick	devt	50000	5000000						3	0.256
2019-10-22T02:48:57	BadAtMath	NewPC	50000	5000000						3	0.256
2022-01-20T18:10:23	MarkS	desktop-i7	50000	5000000	27498139270545223861439	74.542	2	2	4031902225924323	2	0.171
2022-03-02T00:27:28	Dylan Delgado	colab	50000	6750000						7	0.683

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	0C46188FF6E46EAE	0.141

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

0C46188FF6E46EAE

0.141

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T17:19:56

Oliver Kruse

GTX-1

1136665840891657913

5C676B4FA1E10C__

2017-11-18T06:28:53

kkmrkkblmbrbk

c4.xlarge

1136665840891657913

5C676B4FA1E10C__

2022-01-20T19:33:25

SRJ2877

LTOS

1136665840891657913

27498139270545223861439

ECEE44A1DEB6B26C

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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