M21708209 Mersenne number exponent details

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M21708209

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is 2 ^21708209 - 1

has 6534823 decimal digits

takes 15.384 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	2⁶⁸	2.7457	63.2353%	-	-	-	-	2.7457	63.2353%	0.0000%
PrimeNet	2⁶⁵	0.3361	61.5385%	100000	3200000	0.2763	5.1313%	0.6124	63.5120%	1.9736%
GPU72	2⁶⁹	5.4996	63.7681%	160000	4500000	0.4074	3.8397%	5.9070	65.1593%	1.3912%
Difference	-1	-2.7539	-0.5328%	-160000	-4500000	-0.4074	-3.8397%	-3.1613	-1.9240%	-1.9240%

Known prime factors (2 factors, 85.6 bits, 0.00039430% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
21708209	173665673	9	27.372	4 2²	-	4	4	8.244e-13	4.110e-6	8.365e-6
21708209	336588969741400609	18	58.224	7752573456 2⁴ × 3 × 161511947	2015-08-19	16	161511947	0.0021	9.0424	16.889

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
21708209	173665673 336588969741400609	58453949954516972724594857	26	85.596

P-1 results:
No P-1 results for M21708209

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-08-19T11:22:00	TJAOI	Manual testing	2⁵⁸	2⁵⁹*	336588969741400609	58.224	18	0.000	31.69	0.001
2022-06-24T04:22:34	LordJulius	Manual testing	2¹	2⁶⁵	173665673	27.372	9	8.24376e-13	31.69	1.69817e-12
2022-06-24T04:22:34	LordJulius	Manual testing	2¹	2⁶⁵	336588969741400609	58.224	18	0.002	31.69	0.004
2022-06-24T04:22:34	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.344	-	-
2022-06-24T04:22:34	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.688	-	-
2022-04-11T20:17:44	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.377	-	-

ECM factoring results:
No ECM results for M21708209

Lucas-Lehmer results:
No L-L results for M21708209

PRP results:
No PRP results for M21708209

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁹

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-06-24T04:22:34+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