M4734167 Mersenne number exponent details

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M4734167

<<<

>>>

is 2 ^4734167 - 1

has 1425127 decimal digits

takes 0.623 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	6.2765	65.6716%	-	-	-	-	6.2765	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0649	62.2951%	20000	400000	0.0078	3.1258%	0.0727	63.4737%	1.1786%
GPU72	2⁶⁵	1.5411	64.6154%	30000	650000	0.0122	2.2813%	1.5532	65.4226%	0.8072%
Difference	+2	+4.7354	+1.0563%	-30000	-650000	-0.0122	-2.2813%	+4.7232	+0.2490%	+0.2490%

Known prime factors (2 factors, 126.4 bits, 0.00266967% 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
4734167	17704730688147463	17	53.975	1869888693 3 × 61 × 10217971	-	61	10217971	0.0005	0.1063	0.1985
4734167	6281226296632670428663	22	72.412	663392978810493 3 × 2459 × 21169 × 4248061	2019-05-02	21169	4248061	219.19	0.0480	0.0825

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
4734167	17704730688147463 6281226296632670428663	111207419973191279675120274389565931969	39	126.387

P-1 results:
No P-1 results for M4734167

Trial Factoring results:
No TF results for M4734167

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.592 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.592 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	6281226296632670428663	3	0.592

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-05-02T19:33:29	MarkS	laptop64	50000	5000000	6281226296632670428663	72.412	3	2		3	0.592

Lucas-Lehmer results:
No L-L results for M4734167

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T16:59:13

kkmrkkblmbrbk

Manual testing

17704730688147463

8616AD2232AFA5__

2018-03-13T04:34:13

Dt12

AMD_A6-9220

17704730688147463

8616AD2232AFA5__

2019-05-03T20:33:12

trebor

Laptop

17704730688147463

6281226296632670428663

D6400FD7B3E94ACA

2019-05-03T21:30:24

ATH

ec2-PRPCFDC

17704730688147463

6281226296632670428663

D6400FD7B3E94ACA

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-05-03T21:30:24+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