M1374019 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	21.6256	68.6567%	500000	15000000	0.0714	4.8961%	21.6970	70.1913%	1.5346%
PrimeNet	2⁵⁶	0.0070	62.5000%	6000	100000	0.0006	2.6222%	0.0076	63.4833%	0.9833%
GPU72	2⁶⁰	0.1118	65.0000%	5500	60000	0.0005	1.1387%	0.1123	65.3985%	0.3985%
Difference	+7	+21.5138	+3.6567%	+494500	+14940000	+0.0709	+3.7574%	+21.5847	+4.7928%	+4.7928%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.6256

68.6567%

500000

15000000

0.0714

4.8961%

21.6970

70.1913%

1.5346%

PrimeNet

2⁵⁶

0.0070

62.5000%

6000

100000

0.0006

2.6222%

0.0076

63.4833%

0.9833%

GPU72

2⁶⁰

0.1118

65.0000%

5500

60000

0.0005

1.1387%

0.1123

65.3985%

0.3985%

Difference

+21.5138

+3.6567%

+494500

+14940000

+0.0709

+3.7574%

+21.5847

+4.7928%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1374019	1376767039	10	30.359	501 3 × 167	-	3	167	1.154e-10	6.608e-7	9.225e-7
1374019	44091991622080014948847	23	75.223	16044898804921917 3² × 7 × 254680933411459	2018-07-20	9	254680933411459	6,505.6	768,185	1,434,755

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1374019

1376767039

30.359

501
3 × 167

167

1.154e-10

6.608e-7

9.225e-7

1374019

44091991622080014948847

75.223

16044898804921917
3² × 7 × 254680933411459

2018-07-20

254680933411459

6,505.6

768,185

1,434,755

exponent	prime factors	composite factor	digits	bits*
1374019	1376767039 44091991622080014948847	60704400749143909202199820654033	32	105.582

exponent

prime factors

composite factor

digits

bits*

1374019

1376767039
44091991622080014948847

60704400749143909202199820654033

105.582

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:05:30	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1376767039	-	-	0.071	-	-	4.896%

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.369 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:	25.369 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.278	0.000%
25	50000	1.358	25.726%
30	250000	0.113	89.312%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		3	0.088
50000	5000000		250	11.73
50000	5000000	44091991622080014948847	1	0.047
250000	35000000		50	13.51

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-13T19:42:42	Chang Chia-Tche	exbpc13	50000	5000000						3	0.141
2018-07-20T22:33:54	Chang Chia-Tche	exbpc13	50000	5000000	44091991622080014948847	75.223	1	2		1	0.047
2018-09-21T11:53:33	storm5510	HP-Z220-CMT	50000	50000						3	0.088
2018-11-02T13:34:29	TJAOI	Manual testing	50000	5000000						247	11.58
2021-07-30T10:25:02	TJAOI	Manual testing	250000	35000000						50	13.51

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T11:06:54

Oliver Kruse

GTX-2

1376767039

0DA609CDB3C81E__

2017-10-25T17:29:25

kkmrkkblmbrbk

c4.xlarge

1376767039

0DA609CDB3C81E__

2018-07-21T22:23:25

Gabriel Lignelli

6300

1376767039

44091991622080014948847

769B9F6A942AB8__

2018-07-22T17:40:03

Battlemaxx

Work-3

1376767039

44091991622080014948847

769B9F6A942AB8__

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

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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