M3259561 Mersenne number exponent details

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M3259561

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is 2 ^3259561 - 1

has 981226 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	-unknown-	-unknown-
PRP	C2E37971C0C657D6	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	36.6266	68.1159%	4000000	150000000	1.8206	8.1130%	38.4472	70.7027%	2.5867%
PrimeNet	2⁶⁰	0.0471	63.3333%	14000	260000	0.0042	2.7723%	0.0513	64.3498%	1.0165%
GPU72	2⁶⁴	1.0920	65.6250%	16000	280000	0.0046	1.6558%	1.0966	66.1942%	0.5692%
Difference	+5	+35.5347	+2.4909%	+3984000	+149720000	+1.8159	+6.4572%	+37.3506	+4.5085%	+4.5085%

Known prime factors (1 factor, 73.9 bits, 0.00226673% 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
3259561	17446446998699419901183	23	73.885	2676195812672231 103 × 25982483618177	2021-05-26	103	25982483618177	626.35	215,582	402,647

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-05T16:47:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.670%
2011-09-14T12:40:00	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.696%
2014-06-11T02:12:00	Jocelyn Larouche	Manual testing	79691	79691		-		-	-	0.012	-	-	0.651%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	99382	99382		-		-	-	0.015	-	-	0.746%
2016-01-19T03:09:25	Jocelyn Larouche	Manual testing	415800	4158000	6	-		-	-	0.094	-	-	3.335%
2020-09-12T12:21:47	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.113%
2022-04-02T19:48:44	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.012%

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	-	-
2009-04-04T07:04:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-22T06:35:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.094	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.301	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.602	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.146	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.293	-	-
2017-03-30T02:15:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.585	-	-
2019-01-07T14:44:13	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.170	-	-
2021-02-07T12:22:14	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.34	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.925 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	6.925 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.726	17.791%
25	50000	0.165	84.765%
30	250000	0.011	98.918%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	4.218
50000	6450000		3	0.493
50000	6700000	17446446998699419901183	5	0.838
80000	11280000		5	1.377

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-01T20:05:00	Stun	Core2	50000	5000000						3	0.436
2011-11-12T10:27:00	Aldo_Grid	Negozietto	50000	5000000						3	0.436
2014-06-15T13:38:00	Bruce	fx6840-21	50000	5000000						3	0.436
2016-09-03T04:22:27	Richard Kint	Desktop	50000	5000000						3	0.436
2018-12-26T04:29:02	volki	home	50000	5000000						3	0.436
2020-12-31T05:16:41	axn	Manual testing	50000	6450000						3	0.493
2021-01-25T00:48:46	Zenzoma	AMD3970X	50000	5000000						7	1.018
2021-01-25T09:23:54	axn	Manual testing	80000	11280000						5	1.377
2021-04-05T13:36:08	mnd9	50869	50000	5000000						7	1.018
2021-05-26T06:51:44	kutens	terra	50000	6700000	17446446998699419901183	73.885	5	2	2809465844876612	5	0.838

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	Wojciech Florek	v4_computers	3782703B0D9058__	0.342

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-28T04:06:26

kutens

canopus

17446446998699419901183

C2E37971C0C657D6

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 = 99382 (P-1 stage 1)

B1 = 79691 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10¹

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10⁶

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10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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10¹⁴

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:44+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