M84557219 Mersenne number exponent details

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M84557219

<<<

is 2 ^84557219 - 1

has 25454260 decimal digits

takes 263.860 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	2⁷⁶	180.9898	64.4737%	670000	12395000	5.9220	3.3692%	186.9118	65.6706%	1.1970%
PrimeNet	2⁷¹	5.6539	61.9718%	360000	17000000	5.7310	5.3778%	11.3849	64.0169%	2.0451%
GPU72	2⁷⁵	90.4939	64.0000%	550000	19000000	7.0369	3.9416%	97.5307	65.4190%	1.4190%
Difference	+1	+90.4959	+0.4737%	+120000	-6605000	-1.1149	-0.5724%	+89.3811	+0.2517%	+0.2517%

Known prime factors (1 factor, 106.3 bits, 0.00012569% 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
84557219	98272228738510755321309371330593	32	106.277	581098987766560506923184 2⁴ × 3 × 19 × 32887 × 42299 × 247691 × 1849229	2017-11-21	247691	1849229	1.690e+9	1.5155	2.2809

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2017-11-22T01:27:02	Jwb52z	Clay	670000	12395000			98272228738510755321309371330593	32	106.277	5.922	527.7	11.84	3.369%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2010-12-09T02:20:00	Architects Cubed	m1_54	2⁶⁴	2⁶⁵		-	-	0.044	-	-
2012-08-13T07:29:00	Carsten Kossendey	Manual testing	2⁶⁵	2⁶⁶		-	-	0.088	-	-
2013-08-18T09:22:00	Robish	Manual testing	2⁶⁶	2⁶⁷		-	-	0.177	-	-
2013-08-18T16:11:00	Robish	Manual testing	2⁶⁷	2⁶⁸		-	-	0.353	-	-
2013-08-19T17:42:00	Robish	Manual testing	2⁶⁸	2⁶⁹		-	-	0.707	-	-
2013-08-20T18:17:00	Robish	Manual testing	2⁶⁹	2⁷⁰		-	-	1.414	-	-
2014-09-13T00:27:00	SMoffat	Manual testing	2⁷⁰	2⁷¹		-	-	2.828	-	-
2017-02-04T00:47:48	ANONYMOUS	Manual testing	2⁷¹	2⁷²		-	-	5.656	-	-
2017-02-04T00:47:48	ANONYMOUS	Manual testing	2⁷²	2⁷³		-	-	11.31	-	-
2017-02-04T00:47:48	ANONYMOUS	Manual testing	2⁷³	2⁷⁴		-	-	22.62	-	-
2017-05-05T20:37:45	ktony	Manual testing	2⁷⁴	2⁷⁵		-	-	45.25	-	-
2017-05-05T20:37:45	ktony	Manual testing	2⁷⁵	2⁷⁶		-	-	90.50	-	-

ECM factoring results:
No ECM results for M84557219

Lucas-Lehmer results:
No L-L results for M84557219

PRP results:
No PRP results for M84557219

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 = 670000, B2 = 12395000 (P-1 stage 2)

B1 = 670000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁶

2⁷⁵

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2017-11-22T01:27:02+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