M1422709 Mersenne number exponent details

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M1422709

<<<

>>>

is 2 ^1422709 - 1

has 428279 decimal digits

takes 0.054 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	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	20.8854	68.6567%	500000	15000000	0.0714	4.9168%	20.9569	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	+20.7775	+3.6567%	+494000	+14920000	+0.0709	+3.6146%	+20.8484	+4.7420%	+4.7420%

Known prime factors (1 factor, 27.6 bits, 0.00193926% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1422709	202024679	9	27.590	71 71	-	1	71	1.276e-11	2.665e-7	4.235e-7

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	-	skipped known factor: 202024679	-	-	0.071	-	-	4.917%

Trial Factoring results:
No TF results for M1422709

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	14.654	0.000%
25	50000	1.674	18.740%
30	250000	0.144	86.623%
35	1000000	0.010	99.005%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.84
250000	40000000		50	14.50

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-18T12:55:05	Oliver Kruse	ECM-HTC	50000	5000000						3	0.142
2018-09-18T20:30:04	Ra1nb0w	ra1nb0w_H	50000	5000000						3	0.142
2019-01-18T13:09:04	TJAOI	Manual testing	50000	5000000						245	11.56
2022-03-10T10:37:56	TJAOI	Manual testing	250000	40000000						50	14.50

Lucas-Lehmer results:
No L-L results for M1422709

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T20:16:12

Oliver Kruse

GTX-3

202024679

5F9A0206806EC2__

2017-10-26T14:23:24

kkmrkkblmbrbk

c4.xlarge

202024679

5F9A0206806EC2__

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

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-10T10:37:56+00:00

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