M3833009 Mersenne number exponent details

≡

M3833009

<<<

>>>

is 2 ^3833009 - 1

has 1153851 decimal digits

takes 0.403 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	C3BD8220224415B1	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	2⁶⁷	7.7521	67.1642%	200000	130364850	1.1105	6.8283%	8.8626	69.4063%	2.2421%
PrimeNet	2⁶⁰	0.0401	63.3333%	17000	340000	0.0053	3.1926%	0.0453	64.5040%	1.1706%
GPU72	2⁶⁴	0.9286	65.6250%	24000	500000	0.0076	2.2266%	0.9362	66.3904%	0.7654%
Difference	+3	+6.8235	+1.5392%	+176000	+129864850	+1.1029	+4.6018%	+7.9264	+3.0159%	+3.0159%

Known prime factors (1 factor, 72.5 bits, 0.00189248% 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
3833009	6860490792869448265207	22	72.539	894922343369067 3 × 13 × 19 × 179 × 6747052853	2016-03-24	179	6747052853	341.70	55.982	104.56

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-27T16:13:00	Carsten Kossendey	leela	20000	270000		-		-	-	0.005	-	-	1.162%
2011-10-30T01:06:00	Squeeky_Squirrel	T7500_2200	70000	1137500		-		-	-	0.020	-	-	2.369%
2014-10-17T00:38:00	Jocelyn Larouche	Manual testing	86745	86745		-		-	-	0.013	-	-	0.945%
2016-02-17T12:20:49	Jocelyn Larouche	Manual testing	219542	2195420	6	-		-	-	0.050	-	-	3.348%
2020-10-02T12:37:11	Jocelyn Larouche	Manual testing	383300	3833009	6	-		-	-	0.087	-	-	4.070%
2022-05-25T14:13:45	Jocelyn Larouche	Manual testing	200000	130364850		-		-	-	1.110	-	-	6.828%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.040	-	-
2009-02-26T15:59:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.040	-	-
2011-03-09T12:11:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.080	-	-
2012-04-20T00:55:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.416	-	-
2016-02-23T16:29:40	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.256	-	-
2015-01-18T20:59:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.512	-	-
2015-01-18T20:59:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.975	-	-
2016-03-07T09:18:44	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.950	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.201 GHz-days
Estimated T-Level:	0.400

Digits	B1	Curves	Complete	FacMiss
20	11000	8 / 100	0.080	92.274%
25	50000	8 / 280	0.029	97.178%

New Calculation Method

Total ECM effort:	1.201 GHz-days
Estimated T-Level:	0.400

Digits	B1	Complete	FacMiss
20	11000	0.308	73.514%
25	50000	0.028	97.193%
30	250000	0.002	99.821%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.901
50000	5000000	6860490792869448265207	2	0.300

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-20T10:32:00	Aare Vesi	t0	50000	5000000						3	0.450
2012-08-26T10:42:00	oodaira	Linux01	50000	5000000						3	0.450
2016-03-24T14:22:43	Sid & Andy	Mrs_Potato_Head	50000	5000000	6860490792869448265207	72.539	2	2		2	0.300

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-11T00:00:00	ANONYMOUS	v4_computers	C3BD8220224415B1	0.403
1999-09-14T00:00:00	ANONYMOUS	v4_computers	C3BD8220224415B1	0.403

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T18:03:10

kkmrkkblmbrbk

Manual testing

6860490792869448265207

AF61D76F54F6CF__

2017-12-17T10:41:22

Oliver Kruse

GTX-3

6860490792869448265207

AF61D76F54F6CF__

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 = 200000, B2 = 130364850 (P-1 stage 2)

B1 = 383300, B2 = 3833009 (P-1 stage 2)

B1 = 383300 (P-1 stage 1)

B1 = 219542, B2 = 2195420 (P-1 stage 2)

B1 = 219542 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 70000, B2 = 1137500 (P-1 stage 2)

B1 = 86745 (P-1 stage 1)

B1 = 70000 (P-1 stage 1)

B1 = 20000, B2 = 270000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-25T14:13:45+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