M78208159 Mersenne number exponent details

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M78208159

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is 2 ^78208159 - 1

has 23543002 decimal digits

takes 244.047 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	2⁷⁴	48.9190	63.5135%	715000	13227500	6.3197	4.1379%	55.2387	65.0233%	1.5098%
PrimeNet	2⁷¹	6.1129	61.9718%	320000	16000000	5.3133	5.1913%	11.4262	63.9460%	1.9741%
GPU72	2⁷⁵	97.8403	64.0000%	500000	17000000	6.3299	3.7721%	104.1702	65.3580%	1.3580%
Difference	-1	-48.9213	-0.4865%	+215000	-3772500	-0.0102	+0.3658%	-48.9315	-0.3347%	-0.3347%

Known prime factors (1 factor, 82.3 bits, 0.00010524% 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
78208159	5980644118600514360767129	25	82.307	38235423228671796 2² × 3 × 19 × 283 × 124769 × 4749391	2015-05-10	124769	4749391	20,591	1.7046	2.1868

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2015-05-10T10:55:00	Jwb52z	Clay	715000	13227500			5980644118600514360767129	25	82.307	6.320	488.1	12.64	4.138%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2004-03-16T00:00:00	AxelFox	v4_computers	2¹	2⁶²		-	-	0.008	-	-
2008-05-21T00:00:00	1997rj7	v4_computers	2¹	2⁶⁴		-	-	0.046	-	-
2010-12-22T16:10:00	ANONYMOUS		2⁶⁴	2⁶⁵		-	-	0.048	-	-
2011-01-17T18:42:00	ANONYMOUS		2⁶⁵	2⁶⁶		-	-	0.096	-	-
2011-01-17T23:01:00	sannerud.com	JimEmcLap	2⁶⁶	2⁶⁷		-	-	0.191	-	-
2011-01-18T03:33:00	sannerud.com	JimEmcLap	2⁶⁷	2⁶⁸		-	-	0.382	-	-
2011-01-18T08:48:00	sannerud.com	JimEmcLap	2⁶⁸	2⁶⁹		-	-	0.764	-	-
2011-01-19T23:21:00	sannerud.com	JimEmcLap	2⁶⁹	2⁷⁰		-	-	1.529	-	-
2014-02-23T10:08:00	PascalBieri	Manual testing	2⁷⁰	2⁷¹		-	-	3.058	-	-
2014-09-22T14:24:00	NickOfTime	Manual testing	2⁷¹	2⁷²		-	-	6.115	-	-
2014-09-22T14:24:00	NickOfTime	Manual testing	2⁷²	2⁷³		-	-	12.23	-	-
2014-09-22T15:25:00	NickOfTime	Manual testing	2⁷³	2⁷⁴		-	-	24.46	-	-

ECM factoring results:
No ECM results for M78208159

Lucas-Lehmer results:
No L-L results for M78208159

PRP results:
No PRP results for M78208159

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 = 715000, B2 = 13227500 (P-1 stage 2)

B1 = 715000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶²

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2015-05-10T10:55:00+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