M3280229 Mersenne number exponent details

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M3280229

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>>>

is 2 ^3280229 - 1

has 987448 decimal digits

takes 0.345 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	A8B3823EBF40C2E0	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	72.8457	68.5714%	4000000	150000000	1.8206	7.4949%	74.6663	70.9270%	2.3555%
PrimeNet	2⁶⁰	0.0468	63.3333%	14000	260000	0.0042	2.7755%	0.0510	64.3510%	1.0177%
GPU72	2⁶⁴	1.0851	65.6250%	17000	280000	0.0048	1.6873%	1.0899	66.2050%	0.5800%
Difference	+6	+71.7606	+2.9464%	+3983000	+149720000	+1.8158	+5.8076%	+73.5764	+4.7219%	+4.7219%

Known prime factors (1 factor, 92.7 bits, 0.00282561% 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
3280229	7968802974277945381766808049	28	92.686	1214671746130825832856 2³ × 3² × 3670763219 × 4595894617	2022-01-22	3670763219	4595894617	459,042,279	566.70	1,137.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T04:56:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.572%
2011-09-21T10:40:00	harlee	P4_2600	60000	1065000		-		-	-	0.017	-	-	1.496%
2013-09-06T09:36:00	Squeeky_Squirrel	P4_2600	115000	2616250		-		-	-	0.038	-	-	2.181%
2017-01-12T03:13:44	Jocelyn Larouche	low 4M	138000	138000		-		-	-	0.021	-	-	0.788%
2017-01-21T04:21:45	Squeeky_Squirrel	P4_2600	205000	5893750	12	-		-	-	0.078	-	-	2.926%
2017-01-30T01:30:44	Jocelyn Larouche	low 4M	165600	165600		-		-	-	0.025	-	-	0.875%
2017-02-04T18:42:55	Jocelyn Larouche	low 4M	198720	198720		-		-	-	0.030	-	-	0.967%
2018-08-06T19:37:28	Jocelyn Larouche	low 4M	410000	820000		-		-	-	0.066	-	-	1.861%
2018-08-07T17:09:29	Jocelyn Larouche	low 4M	410000	1230000		-		-	-	0.069	-	-	2.140%
2018-08-08T12:55:43	Jocelyn Larouche	low 4M	410000	1640000		-		-	-	0.073	-	-	2.340%
2018-08-08T23:04:23	Jocelyn Larouche	low 4M	410000	2050000		-		-	-	0.076	-	-	2.496%
2018-08-11T22:24:53	Jocelyn Larouche	low 4M	410000	4100000		-		-	-	0.093	-	-	2.991%
2021-02-13T13:46:12	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	7.495%
2022-03-24T08:46:58	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	6.428%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:25	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-03T10:31:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-10-02T20:15:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.094	-	-
2012-11-25T15:11:00	lycorn	Manual testing	2⁶²	2⁶⁵		-	-	2.037	-	-
2015-06-29T20:47:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.278	-	-
2017-04-05T22:02:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.556	-	-
2018-12-03T19:08:42	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.112	-	-
2021-08-02T18:24:31	MadPoo	Manual testing	2⁶⁸	2⁶⁹		-	-	18.22	-	-
2022-01-17T12:09:39	TJAOI	Manual testing	2⁶⁹	2⁷⁰		-	-	36.45	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.644 GHz-days
Estimated T-Level:	3.550

Digits	B1	Curves	Complete	FacMiss
20	11000	71 / 100	0.710	48.989%
25	50000	71 / 280	0.254	77.567%

New Calculation Method

Total ECM effort:	10.644 GHz-days
Estimated T-Level:	3.550

Digits	B1	Complete	FacMiss
20	11000	2.330	9.729%
25	50000	0.210	81.042%
30	250000	0.013	98.712%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		50	7.280
50000	5000000	7968802974277945381766808049	7	1.019
50000	6550000		7	1.161
50000	6800000		7	1.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-23T16:55:00	Csaba Vágó	work-laptop	50000	5000000						3	0.437
2011-10-04T11:51:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.437
2014-08-18T08:58:00	fireredd	ont111	50000	5000000						3	0.437
2016-09-10T23:03:37	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-02-05T13:18:29	IanGlencross	glenx24	50000	5000000						3	0.437
2021-01-22T09:18:19	mat10243x	K	50000	5000000						7	1.019
2021-02-20T00:56:54	Zenzoma	AM3700X_1	50000	5000000						7	1.019
2021-03-23T02:52:09	Zenzoma	AMD3970X	50000	5000000						7	1.019
2021-05-17T17:04:55	kutens	terra	50000	6550000						7	1.161
2021-06-22T18:33:41	LaurV	Zero818	50000	6800000						7	1.184
2021-08-09T01:49:20	Anton Evers	windows_laptop	50000	5000000						7	1.019
2021-10-17T23:14:33	RIHATEC	i7-3770K	50000	5000000						7	1.019
2022-01-22T20:55:34	daveward2005	d12436	50000	5000000	7968802974277945381766808049	92.686	7	2	2853108831409738	7	1.019

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	D459077A6BB15A__	0.345

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-01-29T08:09:18

LaurV

debi

7968802974277945381766808049

A8B3823EBF40C2E0

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

B1 = 205000, B2 = 5893750 (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 = 410000, B2 = 820000 (P-1 stage 2)

B1 = 410000 (P-1 stage 1)

B1 = 115000, B2 = 2616250 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

B1 = 198720 (P-1 stage 1)

B1 = 165600 (P-1 stage 1)

B1 = 138000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-24T08:46:58+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