M4659181 Mersenne number exponent details

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M4659181

<<<

>>>

is 2 ^4659181 - 1

has 1402554 decimal digits

takes 0.613 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	6.3775	65.6716%	-	-	-	-	6.3775	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0659	62.2951%	20000	400000	0.0078	3.1173%	0.0737	63.4705%	1.1754%
GPU72	2⁶⁵	1.5659	64.6154%	30000	600000	0.0117	2.2293%	1.5775	65.4042%	0.7888%
Difference	+2	+4.8116	+1.0563%	-30000	-600000	-0.0117	-2.2293%	+4.8000	+0.2674%	+0.2674%

Known prime factors (2 factors, 104.0 bits, 0.00223228% 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
4659181	234487261369	12	37.771	25164 2² × 3³ × 233	-	27	233	5.685e-9	7.297e-6	1.049e-5
4659181	86843750364637313977	20	66.235	9319636902348 2² × 3⁶ × 67 × 83 × 574723	2019-03-17	729	574723	5.5776	0.0061	0.0112

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
4659181	234487261369 86843750364637313977	20363753190016898897414915854513	32	104.006

P-1 results:
No P-1 results for M4659181

Trial Factoring results:
No TF results for M4659181

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.590 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:	0.590 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	86843750364637313977	3	0.590

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-03-17T04:18:10	ATH	ec2-ECMCF	50000	5000000	86843750364637313977	66.235	3	2		3	0.590

Lucas-Lehmer results:
No L-L results for M4659181

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:15:21

kkmrkkblmbrbk

Manual testing

234487261369

75D411BA46C6DF__

2018-04-04T23:17:39

Oliver Kruse

GTX-7

234487261369

75D411BA46C6DF__

2019-03-18T06:03:16

J.R. Allen

aofafujitsu

234487261369

86843750364637313977

6B3CE75705F06413

2019-03-19T04:23:31

marssystems

SYSTEM01

234487261369

86843750364637313977

6B3CE75705F06413

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

TF factor-bounds graph:

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-03-19T04:23:31+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