M1380619 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	21.5222	68.6567%	500000	15000000	0.0714	4.8990%	21.5936	70.1922%	1.5355%
PrimeNet	2⁵⁶	0.0070	62.5000%	6500	110000	0.0007	2.7547%	0.0076	63.5330%	1.0330%
GPU72	2⁶⁰	0.1112	65.0000%	5500	65000	0.0005	1.1709%	0.1117	65.4098%	0.4098%
Difference	+7	+21.4109	+3.6567%	+494500	+14935000	+0.0709	+3.7280%	+21.4819	+4.7824%	+4.7824%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.5222

68.6567%

500000

15000000

0.0714

4.8990%

21.5936

70.1922%

1.5355%

PrimeNet

2⁵⁶

0.0070

62.5000%

6500

110000

0.0007

2.7547%

0.0076

63.5330%

1.0330%

GPU72

2⁶⁰

0.1112

65.0000%

5500

65000

0.0005

1.1709%

0.1117

65.4098%

0.4098%

Difference

+21.4109

+3.6567%

+494500

+14935000

+0.0709

+3.7280%

+21.4819

+4.7824%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1380619	4089393479	10	31.929	1481 1481	-	1	1481	2.736e-10	4.519e-6	8.341e-6
1380619	9953241102591571721	19	63.110	3604629916940 2² × 5 × 13 × 1327 × 10447597	2015-01-11	1327	10447597	2.2149	0.0316	0.0589
1380619	54473285552787680079870529	26	85.494	19727848723213167456 2⁵ × 3 × 199 × 2441 × 6047 × 69959657	2018-11-09	6047	69959657	7,562,451	0.2113	0.3941
1380619	71962218452990737443874903	26	85.895	26061577615906610529 3 × 8687192538635536843	2018-11-09	3	8687192538635536843	10,477,606	2.620e+10	4.894e+10

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1380619

4089393479

31.929

1481
1481

1481

2.736e-10

4.519e-6

8.341e-6

1380619

9953241102591571721

63.110

3604629916940
2² × 5 × 13 × 1327 × 10447597

2015-01-11

1327

10447597

2.2149

0.0316

0.0589

1380619

54473285552787680079870529

85.494

19727848723213167456
2⁵ × 3 × 199 × 2441 × 6047 × 69959657

2018-11-09

6047

69959657

7,562,451

0.2113

0.3941

1380619

71962218452990737443874903

85.895

26061577615906610529
3 × 8687192538635536843

2018-11-09

8687192538635536843

10,477,606

2.620e+10

4.894e+10

exponent	prime factors	composite factor	digits	bits*
1380619	4089393479 9953241102591571721	40702719259852743396218207359	29	95.039
1380619	4089393479 54473285552787680079870529	222762698719274849190160740456880391	36	117.423
1380619	4089393479 71962218452990737443874903	294281826876033789750383156819957537	36	117.825
1380619	9953241102591571721 54473285552787680079870529	542185744757213983333181036333729384297710409	45	148.604
1380619	9953241102591571721 71962218452990737443874903	716257310539981076168879790832595323276418063	45	149.005
1380619	54473285552787680079870529 71962218452990737443874903	39200184748018513351699683644090246713374363124336 87	52	171.389
1380619	4089393479 9953241102591571721 54473285552787680079870529	22172108490169093016503252143096150118977419411950 22911	55	180.533
1380619	4089393479 9953241102591571721 71962218452990737443874903	29290579750082765816684193193656992956524809413100 11177	55	180.935
1380619	4089393479 54473285552787680079870529 71962218452990737443874903	16030497988414216667171511986050561179717430264644 126237727073	62	203.318
1380619	9953241102591571721 54473285552787680079870529 71962218452990737443874903	39016889006316110090397633609008264311336814288976 833668877363916965327	71	234.499
1380619	4089393479 9953241102591571721 54473285552787680079870529 71962218452990737443874903	15955541147329589041631818339770963173188919412597 5885187574737252747905702902633	81	266.428

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-01-11T14:36:00	alpertron	Manual testing	500000	15000000	12		9953241102591571721	19	63.110	0.071	0.105	0.143	4.899%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-01-11T14:36:00

alpertron

Manual testing

500000

15000000

9953241102591571721

63.110

0.071

0.105

0.143

4.899%

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.303 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:	25.303 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		218	10.23
50000	5000000	54473285552787680079870529	32	1.502
50000	5000000	71962218452990737443874903	1	0.047
250000	35000000		50	13.52

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-13T23:40:11	storm5510	7700_Kaby_Lake	50000	5000000						3	0.141
2018-07-29T18:19:46	Chang Chia-Tche	exbpc13	50000	5000000						3	0.141
2018-11-09T13:47:20	TJAOI	Manual testing	50000	5000000	54473285552787680079870529	85.494	32	2		32	1.502
2018-11-09T13:47:20	TJAOI	Manual testing	50000	5000000	71962218452990737443874903	85.895	1	2		1	0.047
2018-11-09T13:47:20	TJAOI	Manual testing	50000	5000000						212	9.95
2021-09-17T08:20:11	TJAOI	Manual testing	250000	35000000						50	13.52

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T00:01:44

Oliver Kruse

GTX-0

4089393479

9953241102591571721

9B71A7C327C0D5__

2017-10-24T20:14:52

kkmrkkblmbrbk

old

4089393479

9953241102591571721

9B71A7C327C0D5__

2018-11-09T14:53:26

rucio

4089393479

9953241102591571721

54473285552787680079870529

71962218452990737443874903

B860D7BE19B521__

2018-11-09T15:31:55

ATH

ec2-PRPCFDC

4089393479

9953241102591571721

54473285552787680079870529

71962218452990737443874903

B860D7BE19B521__

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

10¹⁶

10¹⁷

10¹⁸

10¹⁹

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