M1343197 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	22.1218	68.6567%	500000	15000000	0.0714	4.8827%	22.1932	70.1871%	1.5304%
PrimeNet	2⁵⁶	0.0071	62.5000%	6000	100000	0.0006	2.6104%	0.0078	63.4789%	0.9789%
GPU72	2⁶⁰	0.1143	65.0000%	5500	40000	0.0004	0.9805%	0.1148	65.3432%	0.3432%
Difference	+7	+22.0074	+3.6567%	+494500	+14960000	+0.0710	+3.9022%	+22.0784	+4.8439%	+4.8439%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.1218

68.6567%

500000

15000000

0.0714

4.8827%

22.1932

70.1871%

1.5304%

PrimeNet

2⁵⁶

0.0071

62.5000%

6000

100000

0.0006

2.6104%

0.0078

63.4789%

0.9789%

GPU72

2⁶⁰

0.1143

65.0000%

5500

40000

0.0004

0.9805%

0.1148

65.3432%

0.3432%

Difference

+22.0074

+3.6567%

+494500

+14960000

+0.0710

+3.9022%

+22.0784

+4.8439%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1343197	11250811492369	14	43.355	4188072 2³ × 3 × 7 × 97 × 257	-	97	257	1.317e-6	5.853e-6	1.093e-5
1343197	165527990412193	15	47.234	61617168 2⁴ × 3² × 449 × 953	2008-08-26	449	953	1.465e-5	2.638e-5	5.059e-5
1343197	2022043593720843894401	22	70.776	752698075457600 2⁶ × 5² × 2237 × 210297853	2017-11-10	2237	210297853	259.59	0.6344	1.1847

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1343197

11250811492369

43.355

4188072
2³ × 3 × 7 × 97 × 257

257

1.317e-6

5.853e-6

1.093e-5

1343197

165527990412193

47.234

61617168
2⁴ × 3² × 449 × 953

2008-08-26

449

953

1.465e-5

2.638e-5

5.059e-5

1343197

2022043593720843894401

70.776

752698075457600
2⁶ × 5² × 2237 × 210297853

2017-11-10

2237

210297853

259.59

0.6344

1.1847

exponent	prime factors	composite factor	digits	bits*
1343197	11250811492369 165527990412193	1862324216838246649784055217	28	90.589
1343197	11250811492369 2022043593720843894401	22749631302305583613147796653325969	35	114.131
1343197	165527990412193 2022043593720843894401	334704812594460125970545591354831393	36	118.010
1343197	11250811492369 165527990412193 2022043593720843894401	3765700752088964396652537779208004209296701140017	49	161.365

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:05:16	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 11250811492369 skipped known factor: 165527990412193	-	-	0.071	-	-	4.883%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T19:53:00	ANONYMOUS	Manual testing	?	?	165527990412193	47.234	15	6.88853e-7	0.111	1.49532e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.180 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.180 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	11.68
50000	5000000	2022043593720843894401	1	0.047
250000	35000000		50	13.45

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-10T14:20:42	Chang Chia-Tche	exbpc13	50000	5000000	2022043593720843894401	70.776	1	2		1	0.047
2017-12-22T00:47:40	Oliver Kruse	ECM-HTC	50000	5000000						3	0.140
2018-07-27T12:48:24	TJAOI	Manual testing	50000	5000000						247	11.54
2021-08-20T12:32:20	TJAOI	Manual testing	250000	35000000						50	13.45

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T06:23:51

Oliver Kruse

GTX-1

11250811492369

165527990412193

C697F8F203BD02__

2017-10-24T07:46:47

kkmrkkblmbrbk

c4.xlarge

11250811492369

165527990412193

C697F8F203BD02__

2017-11-11T06:31:12

Oliver Kruse

GTX-3

11250811492369

165527990412193

2022043593720843894401

E8745BBB671228__

2017-11-11T06:38:55

ATH

ec2-1xf

11250811492369

165527990412193

2022043593720843894401

E8745BBB671228__

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

10⁹

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