M3838613 Mersenne number exponent details

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M3838613

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>>>

is 2 ^3838613 - 1

has 1155538 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	B6AF8A6507687D5D	double-checked
PRP	0FE03C30D53576E0	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	2⁶⁹	31.1015	68.1159%	15000000	750000000	8.3828	11.1423%	39.4843	71.6686%	3.5526%
PrimeNet	2⁶⁰	0.0400	63.3333%	17000	340000	0.0053	3.1934%	0.0453	64.5042%	1.1709%
GPU72	2⁶⁴	0.9272	65.6250%	24000	500000	0.0076	2.2271%	0.9348	66.3906%	0.7656%
Difference	+5	+30.1743	+2.4909%	+14976000	+749500000	+8.3752	+8.9152%	+38.5495	+5.2780%	+5.2780%

Known prime factors (1 factor, 90.4 bits, 0.00235622% 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
3838613	1686706195626621460586308801	28	90.446	219702558662024728800 2⁵ × 3 × 5² × 47 × 101 × 15803 × 1220295757	2021-10-23	15803	1220295757	105,192,889	10.127	18.911

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-27T16:19:00	Carsten Kossendey	leela	20000	270000		-		-	-	0.005	-	-	0.860%
2011-10-28T14:20:00	Squeeky_Squirrel	T7500_2200	70000	1137500		-		-	-	0.020	-	-	1.845%
2014-10-17T00:38:00	Jocelyn Larouche	Manual testing	86721	86721		-		-	-	0.013	-	-	0.708%
2016-02-03T10:08:10	Jocelyn Larouche	Manual testing	239500	2395000	6	-		-	-	0.054	-	-	2.780%
2020-11-22T18:25:15	Carlos Pinho	HomeComputer	173000	4667000	6	-		-	-	0.064	-	-	3.084%
2021-01-31T02:09:37	axn	Manual testing	15000000	750000000		-		-	-	8.383	-	-	11.142%
2022-03-03T00:13:43	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.725%
2022-03-22T17:36:13	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.772%
2022-05-24T23:56:10	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.890%

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	-	-
2009-02-27T17:37:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.040	-	-
2011-03-04T18:43:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.080	-	-
2012-02-20T20:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.416	-	-
2016-02-23T16:29:40	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.256	-	-
2015-01-18T21:00:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.511	-	-
2015-01-18T21:00:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.973	-	-
2016-02-24T12:36:35	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	1.947	-	-
2016-11-21T15:09:25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.893	-	-
2018-09-10T13:18:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.787	-	-
2020-09-07T12:53:25	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	15.57	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.154 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	3.154 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.802
50000	5000000	1686706195626621460586308801	9	1.352

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-23T04:23:00	S00030	vd01	50000	5000000						3	0.451
2012-09-23T21:00:00	Lukasz Wrobel	back	50000	5000000						3	0.451
2016-01-24T22:35:24	Adel El-Atawy	AE2MTV	50000	5000000						3	0.451
2016-01-24T23:12:44	Adel El-Atawy	AE2MTV	50000	5000000						3	0.451
2021-10-23T23:40:01	MarkS	laptop64	50000	5000000	1686706195626621460586308801	90.446	9	2	140558678030668	9	1.352

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	B6AF8A6507687D5D	0.403
2000-06-11T00:00:00	ANONYMOUS	v4_computers	B6AF8A6507687D5D	0.403

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-25T11:09:01

MarkS

laptop64

1686706195626621460586308801

0FE03C30D53576E0

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 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 173000, B2 = 4667000 (P-1 stage 2)

B1 = 239500, B2 = 2395000 (P-1 stage 2)

B1 = 239500 (P-1 stage 1)

B1 = 173000 (P-1 stage 1)

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

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 86721 (P-1 stage 1)

B1 = 70000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-24T23:56:10+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