M3050561 Mersenne number exponent details

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M3050561

<<<

>>>

is 2 ^3050561 - 1

has 918311 decimal digits

takes 0.260 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	D9BC9D6F5D4C6356	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	19.5390	67.6471%	3000000	100000000	1.0224	8.0351%	20.5614	70.2467%	2.5996%
PrimeNet	2⁶⁰	0.0503	63.3333%	12000	220000	0.0029	2.5229%	0.0532	64.2584%	0.9251%
GPU72	2⁶⁴	1.1668	65.6250%	14000	220000	0.0031	1.4650%	1.1699	66.1286%	0.5036%
Difference	+4	+18.3722	+2.0221%	+2986000	+99780000	+1.0193	+6.5701%	+19.3915	+4.1181%	+4.1181%

Known prime factors (1 factor, 72.4 bits, 0.00237452% 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
3050561	6389395517524867072271	22	72.436	1047249262926535 5 × 223 × 939237007109	2020-10-14	223	939237007109	557.48	6,315.2	11,795

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-10-04T14:45:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.665%
2016-03-15T22:19:01	Squeeky_Squirrel	P4_2600	205000	5688750	12	-		-	-	0.062	-	-	3.572%
2017-09-26T04:11:40	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.035%
2021-01-14T13:16:35	Jocelyn Larouche	Manual testing	305056	305056		-		-	-	0.038	-	-	1.534%
2021-01-17T03:41:52	Jocelyn Larouche	Manual testing	305056	3050561	6	-		-	-	0.056	-	-	3.287%
2022-01-23T08:35:01	Jocelyn Larouche	Manual testing	1055056	119912100		-		-	-	0.929	-	-	7.512%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-12T21:13:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-03-18T10:37:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.322	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.644	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.225	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.450	-	-
2017-05-07T02:13:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.899	-	-
2018-07-25T22:30:18	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.80	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.864 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.864 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.516	59.683%
25	50000	0.047	95.442%
30	250000	0.003	99.713%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.747
50000	5000000	6389395517524867072271	1	0.116

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-16T17:14:00	Anu Järvi	Anu	50000	5000000						3	0.349
2011-06-24T23:24:00	Csaba Vágó	apugep	50000	5000000						3	0.349
2013-10-13T00:52:00	Bruce	fx6840-21	50000	5000000						3	0.349
2016-01-31T01:56:21	Bruce	Desk7	50000	5000000						3	0.349
2017-09-04T11:13:19	Bruce	desk	50000	5000000						3	0.349
2020-10-14T05:54:00	mnd9	27016b	50000	5000000	6389395517524867072271	72.436	1	2	4828359136735330	1	0.116

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	ANONYMOUS	v4_computers	D9BC9D6F5D4C6356	0.260

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-17T09:41:03

Sébastien Broucke

Portable_Seb

6389395517524867072271

E17541AA327EE1__

2020-10-20T23:04:51

arnaud

stm-11-010

6389395517524867072271

E17541AA327EE1B3

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1055056, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1055056 (P-1 stage 1)

B1 = 205000, B2 = 5688750 (P-1 stage 2)

B1 = 305056, B2 = 3050561 (P-1 stage 2)

B1 = 305056 (P-1 stage 1)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-23T08:35:01+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