M3439561 Mersenne number exponent details

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M3439561

<<<

>>>

is 2 ^3439561 - 1

has 1035412 decimal digits

takes 0.361 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	BE75E152EFCAD2A2	double-checked
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	17.3292	67.6471%	1000000	114656850	1.0953	7.5156%	18.4245	70.0786%	2.4315%
PrimeNet	2⁶⁰	0.0447	63.3333%	15000	280000	0.0045	2.8998%	0.0491	64.3966%	1.0633%
GPU72	2⁶⁴	1.0348	65.6250%	19000	340000	0.0056	1.8537%	1.0404	66.2622%	0.6372%
Difference	+4	+16.2944	+2.0221%	+981000	+114316850	+1.0898	+5.6619%	+17.3842	+3.8164%	+3.8164%

Known prime factors (1 factor, 66.2 bits, 0.00192560% 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
3439561	86668078763519228207	20	66.232	12598712272223 7 × 11 × 163619639899	2016-12-17	11	163619639899	5.6697	1,357.6	2,535.6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-15T21:06:00	Carsten Kossendey	durandal	15000	210000		-		-	-	0.004	-	-	0.818%
2011-11-03T09:08:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.894%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	78661	78661		-		-	-	0.012	-	-	0.756%
2014-09-17T16:42:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.591%
2021-03-16T16:24:14	Jocelyn Larouche	Manual testing	343956	3783517	6	-		-	-	0.081	-	-	3.565%
2022-01-24T20:13:13	Jocelyn Larouche	Manual testing	1000000	114656850		-		-	-	1.095	-	-	7.516%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:29	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-22T09:56:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-01T12:13:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.089	-	-
2022-05-11T16:04:03	LordJulius	Manual testing	2¹	2⁶²		-	-	0.179	-	-
2012-08-18T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.464	-	-
2016-02-23T16:29:29	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.285	-	-
2022-05-11T16:04:03	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.285	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.571	-	-
2022-05-11T16:04:03	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.571	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.086	-	-
2022-05-11T16:04:03	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.086	-	-
2021-03-16T16:24:16	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.173	-	-
2015-04-14T09:01:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.173	-	-
2022-05-11T16:04:03	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.173	-	-
2022-05-11T16:04:03	LordJulius	Manual testing	2⁶⁶	2⁶⁷	86668078763519228207	66.232	20	1.376	0.734	2.795
2021-06-10T14:05:05	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.690	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.469 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	1.469 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.385	68.071%
25	50000	0.036	96.504%
30	250000	0.002	99.776%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.322
50000	5000000	86668078763519228207	1	0.147

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-04T10:35:00	Sid & Andy	Slinky	50000	5000000						3	0.441
2012-01-21T14:22:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.441
2015-01-26T21:23:00	Sid & Andy	Emperor_Zurg	50000	5000000						3	0.441
2016-12-17T19:17:04	Sid & Andy	Mrs_Potato_Head	50000	5000000	86668078763519228207	66.232	1	2		1	0.147

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	BE75E152EFCAD2A2	0.361

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-06T16:11:57

Oliver Kruse

GTX-0

86668078763519228207

51DE72AA944157__

2017-12-16T11:08:11

kkmrkkblmbrbk

c4.xlarge

86668078763519228207

51DE72AA944157__

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 = 1000000, B2 = 114656850 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 343956, B2 = 3783517 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 343956 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 78661 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 210000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

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10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-11T16:04:03+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