M3205919 Mersenne number exponent details

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M3205919

<<<

>>>

is 2 ^3205919 - 1

has 965078 decimal digits

takes 0.273 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	-unknown-	-unknown-
PRP	A86D56F9D37E9815	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	2⁶⁹	37.2395	68.1159%	4000000	150000000	1.4753	8.1000%	38.7148	70.6985%	2.5826%
PrimeNet	2⁶⁰	0.0479	63.3333%	13000	240000	0.0031	2.6583%	0.0510	64.3081%	0.9747%
GPU72	2⁶⁴	1.1102	65.6250%	16000	260000	0.0036	1.6163%	1.1139	66.1806%	0.5556%
Difference	+5	+36.1293	+2.4909%	+3984000	+149740000	+1.4717	+6.4837%	+37.6010	+4.5180%	+4.5180%

Known prime factors (1 factor, 69.1 bits, 0.00215403% 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
3205919	613865046598606264817	21	69.056	95739325697032 2³ × 11967415712129	2021-01-10	8	11967415712129	71.564	80,466	150,289

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2014-08-21T21:47:00	Jocelyn Larouche	Manual testing	85557	85557		-		-	-	0.011	-	-	0.679%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	105578	105578		-		-	-	0.013	-	-	0.772%
2015-10-02T00:19:36	Squeeky_Squirrel	P4_2600	155000	3952500		-		-	-	0.045	-	-	2.843%
2017-01-30T01:31:05	Jocelyn Larouche	low 4M	186000	186000		-		-	-	0.023	-	-	1.062%
2017-03-23T08:16:46	Squeeky_Squirrel	P4_2600	200000	5550000	12	-		-	-	0.061	-	-	3.199%
2018-07-24T12:57:27	Jocelyn Larouche	low 4M	400000	1598000		-		-	-	0.057	-	-	2.577%
2018-07-25T17:21:12	Jocelyn Larouche	low 4M	400000	3313612		-		-	-	0.069	-	-	3.136%
2018-07-25T21:59:28	Jocelyn Larouche	low 4M	400000	4000000		-		-	-	0.074	-	-	3.282%
2019-12-31T13:48:22	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.100%
2021-01-18T06:10:45	Jocelyn Larouche	Manual testing	420000	3205919	6	-		-	-	0.071	-	-	3.127%
2022-02-07T00:51:02	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.884%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-06T07:08:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-06-21T02:20:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.306	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.612	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.165	-	-
2015-06-21T21:40:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.331	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.331	-	-
2021-02-22T09:03:45	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.662	-	-
2017-03-15T13:25:43	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.662	-	-
2019-01-21T12:54:05	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.324	-	-
2021-12-12T07:47:45	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.697 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	3.697 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	1.124	32.500%
25	50000	0.110	89.607%
30	250000	0.007	99.267%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	2.585
80000	11280000		0	0.00000e+0
80000	11280000	613865046598606264817	5	1.112

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-10T14:13:00	TeamResslerTUB	1062314	50000	5000000						3	0.353
2011-09-03T18:18:00	sannerud.com	JimEmcLW7	50000	5000000						3	0.353
2014-04-27T10:11:00	Lukasz Wrobel	sr-1	50000	5000000						3	0.353
2016-07-25T16:07:22	Dennis Schreiber	z400	50000	5000000						3	0.353
2018-08-12T21:59:52	IanGlencross	glenx24	50000	5000000						3	0.353
2020-12-22T08:11:35	Zenzoma	AMD3970X	50000	5000000						7	0.823
2021-01-10T02:09:18	axn	Manual testing	80000	11280000	613865046598606264817	69.056	5	2	889414915671463	5	1.112
2021-01-10T02:09:18	axn	Manual testing	80000	11280000						0	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	7C6AF178E95A64__	0.273

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-10T14:05:21

EricBock

alux

613865046598606264817

A86D56F9D37E9815

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 = 119912100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 420000, B2 = 3205919 (P-1 stage 2)

B1 = 400000, B2 = 3313612 (P-1 stage 2)

B1 = 200000, B2 = 5550000 (P-1 stage 2)

B1 = 400000, B2 = 1598000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 155000, B2 = 3952500 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 186000 (P-1 stage 1)

B1 = 155000 (P-1 stage 1)

B1 = 105578 (P-1 stage 1)

B1 = 85557 (P-1 stage 1)

10⁰

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10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-07T00:51:02+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