M1422727 Mersenne number exponent details

Residue

Status

L-L

BA5913022F107226

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	20.8852	68.6567%	500000	15000000	0.0714	4.9168%	20.9566	70.1978%	1.5411%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7708%	0.0074	63.5391%	1.0391%
GPU72	2⁶⁰	0.1080	65.0000%	6000	80000	0.0006	1.3022%	0.1085	65.4558%	0.4558%
Difference	+7	+20.7772	+3.6567%	+494000	+14920000	+0.0709	+3.6146%	+20.8481	+4.7420%	+4.7420%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.8852

68.6567%

500000

15000000

0.0714

4.9168%

20.9566

70.1978%

1.5411%

PrimeNet

2⁵⁶

0.0067

62.5000%

6500

110000

0.0007

2.7708%

0.0074

63.5391%

1.0391%

GPU72

2⁶⁰

0.1080

65.0000%

6000

80000

0.0006

1.3022%

0.1085

65.4558%

0.4558%

Difference

+20.7772

+3.6567%

+494000

+14920000

+0.0709

+3.6146%

+20.8481

+4.7420%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1422727	130967146392699191	18	56.862	46026801485 5 × 7 × 1315051471	2001-10-20	7	1315051471	0.0077	3.9665	7.4084
1422727	47359213651025701762409	23	75.326	16643816294702252 2² × 4160954073675563	2017-11-17	4	4160954073675563	10,445	12,550,536	23,440,905

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1422727

130967146392699191

56.862

46026801485
5 × 7 × 1315051471

2001-10-20

1315051471

0.0077

3.9665

7.4084

1422727

47359213651025701762409

75.326

16643816294702252
2² × 4160954073675563

2017-11-17

4160954073675563

10,445

12,550,536

23,440,905

exponent	prime factors	composite factor	digits	bits*
1422727	130967146392699191 47359213651025701762409	6202501067277001019623826217019288511119	40	132.188

exponent

prime factors

composite factor

digits

bits*

1422727

130967146392699191
47359213651025701762409

6202501067277001019623826217019288511119

132.188

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:14:07	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.917%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-20T00:00:00	ANONYMOUS	v4_computers	?	?	130967146392699191	56.862	18	0.001	0.110	0.002
2003-08-25T00:00:00	ANONYMOUS	v4_computers	?	?	130967146392699191	56.862	18	0.001	0.110	0.002

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.343 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:	26.343 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.390	24.916%
30	250000	0.116	89.004%
35	1000000	0.008	99.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	11.70
50000	5000000	47359213651025701762409	3	0.142
250000	40000000		50	14.50

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-18T03:35:35	Chang Chia-Tche	exbpc13	50000	5000000	47359213651025701762409	75.326	3	2		3	0.142
2018-09-18T20:50:16	Ra1nb0w	ra1nb0w_H	50000	5000000						3	0.142
2019-01-25T12:27:16	TJAOI	Manual testing	50000	5000000						245	11.56
2022-03-10T10:37:56	TJAOI	Manual testing	250000	40000000						50	14.50

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T20:24:08

Oliver Kruse

GTX-1

130967146392699191

6AB91B6CFC55AA__

2017-11-04T22:34:31

kkmrkkblmbrbk

c4.xlarge

130967146392699191

6AB91B6CFC55AA__

2017-11-18T14:37:44

kkmrkkblmbrbk

c4.xlarge

130967146392699191

47359213651025701762409

A9227ABD34E3B9__

2017-11-19T03:05:30

Oliver Kruse

Threadripper

130967146392699191

47359213651025701762409

A9227ABD34E3B9__

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

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