M1384619 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	21.4600	68.6567%	500000	15000000	0.0714	4.9007%	21.5314	70.1928%	1.5360%
PrimeNet	2⁵⁶	0.0069	62.5000%	6500	110000	0.0007	2.7562%	0.0076	63.5336%	1.0336%
GPU72	2⁶⁰	0.1109	65.0000%	5500	70000	0.0005	1.2007%	0.1114	65.4202%	0.4202%
Difference	+7	+21.3491	+3.6567%	+494500	+14930000	+0.0709	+3.7000%	+21.4200	+4.7725%	+4.7725%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.4600

68.6567%

500000

15000000

0.0714

4.9007%

21.5314

70.1928%

1.5360%

PrimeNet

2⁵⁶

0.0069

62.5000%

6500

110000

0.0007

2.7562%

0.0076

63.5336%

1.0336%

GPU72

2⁶⁰

0.1109

65.0000%

5500

70000

0.0005

1.2007%

0.1114

65.4202%

0.4202%

Difference

+21.3491

+3.6567%

+494500

+14930000

+0.0709

+3.7000%

+21.4200

+4.7725%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1384619	1165849199	10	30.119	421 421	-	1	421	1.127e-10	1.322e-6	2.369e-6
1384619	541438193460567580788071	24	78.841	195518837117130265 5 × 17² × 167 × 401 × 2020504931	2021-10-28	401	2020504931	64,547	6.0944	11.383

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1384619

1165849199

30.119

421
421

421

1.127e-10

1.322e-6

2.369e-6

1384619

541438193460567580788071

78.841

195518837117130265
5 × 17² × 167 × 401 × 2020504931

2021-10-28

401

2020504931

64,547

6.0944

11.383

exponent	prime factors	composite factor	digits	bits*
1384619	1165849199 541438193460567580788071	631235284154009752147140364105129	33	108.960

exponent

prime factors

composite factor

digits

bits*

1384619

1165849199
541438193460567580788071

631235284154009752147140364105129

108.960

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
unknown			500000	15000000		-	skipped known factor: 1165849199	-	-	0.071	-	-	4.901%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

unknown

500000

15000000

skipped known factor: 1165849199

0.071

-

-

4.901%

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.316 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:	25.316 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.79
250000	35000000		47	12.72
250000	35000000	541438193460567580788071	3	0.812

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-14T08:42:19	storm5510	7700_Kaby_Lake	50000	5000000						3	0.141
2018-08-04T01:25:06	Chang Chia-Tche	exbpc13	50000	5000000						3	0.141
2018-11-16T12:25:45	TJAOI	Manual testing	50000	5000000						245	11.51
2021-10-28T13:36:08	TJAOI	Manual testing	250000	35000000	541438193460567580788071	78.841	3	2		3	0.812
2021-10-28T13:36:09	TJAOI	Manual testing	250000	35000000						47	12.72

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T00:38:53

Oliver Kruse

GTX-0

1165849199

71B1096B4A42F5__

2017-10-25T03:19:05

kkmrkkblmbrbk

old

1165849199

71B1096B4A42F5__

2021-10-29T08:06:21

SRJ2877

LTOS

1165849199

541438193460567580788071

196D44CA4AD8A1FC

2021-10-29T12:15:25

JackBlock

Win10

1165849199

541438193460567580788071

196D44CA4AD8A1FC

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

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