M3255559 Mersenne number exponent details

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M3255559

<<<

>>>

is 2 ^3255559 - 1

has 980021 decimal digits

takes 0.342 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	F7D3E61ABA481BCF	double-checked
PRP	5CF2648B04E08EFF	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	18.3086	67.6471%	4000000	150000000	1.8206	8.7752%	20.1292	70.4861%	2.8390%
PrimeNet	2⁶⁰	0.0472	63.3333%	14000	260000	0.0042	2.7717%	0.0514	64.3496%	1.0163%
GPU72	2⁶⁴	1.0933	65.6250%	16000	280000	0.0046	1.6554%	1.0979	66.1940%	0.5690%
Difference	+4	+17.2153	+2.0221%	+3984000	+149720000	+1.8159	+7.1198%	+19.0313	+4.2921%	+4.2921%

Known prime factors (1 factor, 71.4 bits, 0.00219408% 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
3255559	3179897262906244597247	22	71.429	488379608986697 488379608986697	2021-03-26	1	488379608986697	153.11	4,052,181	7,568,345

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-05T05:40:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.785%
2011-09-13T01:25:00	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.929%
2014-06-11T02:10:00	Jocelyn Larouche	Manual testing	79715	79715		-		-	-	0.012	-	-	0.754%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	99430	99430		-		-	-	0.015	-	-	0.861%
2016-01-17T13:12:29	Jocelyn Larouche	Manual testing	415800	4158000	6	-		-	-	0.094	-	-	3.697%
2020-08-13T13:50:47	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.775%
2022-04-02T19:48:46	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.644%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-03T10:35:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-18T20:19:00	markr	Manual testing	2¹	2⁶²		-	-	0.189	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.302	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.603	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.148	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.295	-	-
2017-03-30T02:15:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.591	-	-
2019-01-07T14:44:15	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.182	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.777 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	4.777 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	0.987	37.280%
25	50000	0.092	91.182%
30	250000	0.006	99.403%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.181
50000	5000000	3179897262906244597247	5	0.727
50000	6450000		3	0.493
80000	11280000		5	1.376

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-19T00:56:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.436
2011-09-21T14:23:00	sannerud.com	Jim2010	50000	5000000						3	0.436
2014-06-09T19:03:00	arnaud	Chamot18	50000	5000000						3	0.436
2016-08-29T01:13:00	f0rteOC	Fortissimo	50000	5000000						3	0.436
2018-12-20T19:26:46	volki	home	50000	5000000						3	0.436
2020-12-31T05:16:36	axn	Manual testing	50000	6450000						3	0.493
2021-01-25T09:23:42	axn	Manual testing	80000	11280000						5	1.376
2021-03-26T10:07:44	daveward2005	Davy	50000	5000000	3179897262906244597247	71.429	5	2	8574274360813117	5	0.727

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-01T00:00:00	ANONYMOUS	v4_computers	F7D3E61ABA481BCF	0.342
1998-02-08T00:00:00	ANONYMOUS	v4_computers	F7D3E61ABA481BCF	0.342
1999-11-04T00:00:00	delta_t	v4_computers	F7D3E61ABA481BCF	0.342

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-03-28T10:19:37

daveward2005

Davy

3179897262906244597247

5CF2648B04E08EFF

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 134316000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 415800, B2 = 4158000 (P-1 stage 2)

B1 = 415800 (P-1 stage 1)

B1 = 60000, B2 = 1050000 (P-1 stage 2)

B1 = 99430 (P-1 stage 1)

B1 = 79715 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

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10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:46+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