M3302149 Mersenne number exponent details

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M3302149

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is 2 ^3302149 - 1

has 994046 decimal digits

takes 0.347 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	BDA0DEA2BBD25A8A	double-checked
PRP	18794DCB96837446	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	2⁷⁰	72.3622	68.5714%	11086738	410209309	5.0000	9.3126%	77.3622	71.4982%	2.9268%
PrimeNet	2⁶⁰	0.0465	63.3333%	14000	260000	0.0042	2.7788%	0.0507	64.3522%	1.0189%
GPU72	2⁶⁴	1.0779	65.6250%	17000	300000	0.0049	1.7224%	1.0828	66.2171%	0.5921%
Difference	+6	+71.2843	+2.9464%	+11069738	+409909309	+4.9951	+7.5902%	+76.2793	+5.2812%	+5.2812%

Known prime factors (1 factor, 76.1 bits, 0.00230579% 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
3302149	83296272154193927232031	23	76.141	12612433926239235 3³ × 5 × 11 × 2879 × 2950059569	2021-01-26	2879	2950059569	7,117.4	24.478	45.717

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T00:38:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.573%
2011-09-29T06:13:00	harlee	P4_2600	55000	880000		-		-	-	0.015	-	-	1.390%
2012-11-13T06:12:00	Squeeky_Squirrel	T7500_2200	205000	4612500		-		-	-	0.068	-	-	2.776%
2018-08-06T19:37:29	Jocelyn Larouche	low 4M	410000	820000		-		-	-	0.066	-	-	1.863%
2018-08-07T17:09:30	Jocelyn Larouche	low 4M	410000	1230000		-		-	-	0.069	-	-	2.142%
2018-08-08T12:55:44	Jocelyn Larouche	low 4M	410000	1640000		-		-	-	0.073	-	-	2.342%
2018-08-08T23:04:23	Jocelyn Larouche	low 4M	410000	2050000		-		-	-	0.076	-	-	2.499%
2018-08-11T22:24:54	Jocelyn Larouche	low 4M	410000	4100000		-		-	-	0.093	-	-	2.993%
2019-12-22T19:53:40	GdS	Manual testing	11086738	410209309	12	-		-	-	5.000	-	-	9.313%
2022-04-02T19:48:42	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	6.433%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-01T15:38:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-13T20:31:00	markr	Manual testing	2¹	2⁶²		-	-	0.186	-	-
2012-08-25T21:54:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.483	-	-
2016-02-23T16:29:25	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.297	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.595	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.131	-	-
2016-02-29T09:31:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.263	-	-
2017-02-21T14:29:04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.526	-	-
2018-12-10T15:07:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.052	-	-
2019-12-13T22:09:33	GdS	Manual testing	2⁶⁸	2⁶⁹		-	-	18.10	-	-
2019-12-13T22:09:33	GdS	Manual testing	2⁶⁹	2⁷⁰		-	-	36.21	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.207 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	3.207 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.710	49.180%
25	50000	0.064	93.787%
30	250000	0.004	99.606%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.187
50000	5000000	83296272154193927232031	7	1.021

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-26T18:13:00	Ryan Schulz	T7400	50000	5000000						3	0.437
2011-10-16T09:24:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.437
2014-07-21T19:52:00	Travis Glenn Russo	i5-spare	50000	5000000						3	0.437
2016-09-23T04:09:48	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-02-25T23:33:32	IanGlencross	glenx24	50000	5000000						3	0.437
2021-01-26T18:14:28	GAN	KL-SCH04	50000	5000000	83296272154193927232031	76.141	7	2		7	1.021

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-17T00:00:00	ANONYMOUS	v4_computers	BDA0DEA2BBD25A8A	0.347
1999-06-15T00:00:00	ANONYMOUS	v4_computers	BDA0DEA2BBD25A8A	0.347

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-26T21:56:29

ViliamF

83296272154193927232031

18794DCB96837446

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 = 11086738, B2 = 410209309 (P-1 stage 2)

B1 = 11086738 (P-1 stage 1)

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

B1 = 1000000 (P-1 stage 1)

B1 = 410000, B2 = 4100000 (P-1 stage 2)

B1 = 410000, B2 = 2050000 (P-1 stage 2)

B1 = 410000, B2 = 1640000 (P-1 stage 2)

B1 = 410000, B2 = 1230000 (P-1 stage 2)

B1 = 205000, B2 = 4612500 (P-1 stage 2)

B1 = 410000, B2 = 820000 (P-1 stage 2)

B1 = 410000 (P-1 stage 1)

B1 = 205000 (P-1 stage 1)

B1 = 55000, B2 = 880000 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:42+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