M3829831 Mersenne number exponent details

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M3829831

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is 2 ^3829831 - 1

has 1152895 decimal digits

takes 0.402 GHz-days to do one PRP test

Last-known PrimeNet details:
0 L-L tests remaining

	Residue	Status
L-L	3A0D35C92079A7BE	double-checked
PRP	CE909B8E0C36E9__	needs double-check

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	31.1729	68.1159%	15000000	750000000	8.3828	11.1403%	39.5557	79.2562%	15.9229%
PrimeNet	2⁶⁰	0.0401	63.3333%	17000	340000	0.0053	3.1921%	0.0454	66.5255%	3.1921%
GPU72	2⁶⁴	0.9294	65.6250%	24000	500000	0.0076	2.2262%	0.9370	67.8512%	2.2262%
Difference	+5	+30.2435	+2.4909%	+14976000	+749500000	+8.3752	+8.9141%	+38.6187	+11.4050%	+11.4050%

Known prime factors (1 factor, 123.3 bits, 0.00322008% 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
3829831	13308178552244110071905903048889185183	38	123.324	1737436789279227996210002875961 37 × 271 × 467 × 60413 × 68771 × 224359 × 398053897	2021-01-21	224359	398053897	3.628e+10	3.3350	6.1686

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-03-17T00:00:00	ANONYMOUS	v4_computers	15000	52500		-		-	-	0.003	-	-	0.421%
2010-09-11T23:55:00	markr	tiny	105000	2257500		-		-	-	0.034	-	-	2.384%
2016-06-14T01:17:15	mikr	MSI	2000000	62000000	12	-		-	-	0.802	-	-	6.786%
2021-01-21T01:42:32	axn	Manual testing	15000000	750000000			13308178552244110071905903048889185183	38	123.324	8.383	0.804	16.77	11.140%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:40	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.040	-	-
2009-02-28T06:59:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.040	-	-
2011-03-11T12:46:00	markr	ut	2⁶¹	2⁶²		-	-	0.080	-	-
2012-02-20T20:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.417	-	-
2016-02-23T16:29:40	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.256	-	-
2015-01-18T20:59:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.513	-	-
2015-01-18T20:59:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.976	-	-
2016-03-05T16:43:34	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.951	-	-
2016-11-20T02:21:04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.902	-	-
2018-09-24T14:19:00	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.805	-	-
2020-08-24T12:45:13	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	15.61	-	-

ECM factoring results:

Total ECM effort:	1.801 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.801

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-21T12:34:00	oodaira	Linux01	50000	5000000						3	0.450
2012-08-23T14:09:00	oodaira	Linux01	50000	5000000						3	0.450
2016-03-29T14:25:33	Sid & Andy	Mrs_Potato_Head	50000	5000000						3	0.450
2017-09-08T09:28:47	bayanne	iMac	50000	5000000						3	0.450

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-03-01T00:00:00	ANONYMOUS	v4_computers	61C536D29134CD__	0.402
2001-03-18T00:00:00	ANONYMOUS	v4_computers	3A0D35C92079A7BE	0.402

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-24T01:21:41

Klaus Nordmann

no1

13308178552244110071905903048889185183

CE909B8E0C36E9__

2021-04-04T17:36:53

ATH

5960X

13308178552244110071905903048889185183

CE909B8E0C36E96A

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 = 15000000, B2 = 750000000 (stage 2)

B1 = 15000000 (stage 1)

B1 = 2000000, B2 = 62000000 (stage 2)

B1 = 2000000 (stage 1)

B1 = 105000, B2 = 2257500 (stage 2)

B1 = 105000 (stage 1)

B1 = 15000, B2 = 52500 (stage 2)

B1 = 15000 (stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2021-04-04T17:36:53+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