M3817783 Mersenne number exponent details

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M3817783

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is 2 ^3817783 - 1

has 1149268 decimal digits

takes 0.401 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	9CF6BF73C02A49E1	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	2⁶⁸	15.6124	67.6471%	100000	130364850	1.0961	5.4297%	16.7085	69.4037%	1.7567%
PrimeNet	2⁶⁰	0.0402	63.3333%	17000	340000	0.0053	3.1904%	0.0455	64.5032%	1.1698%
GPU72	2⁶⁴	0.9323	65.6250%	24000	450000	0.0072	2.1650%	0.9395	66.3692%	0.7442%
Difference	+4	+14.6801	+2.0221%	+76000	+129914850	+1.0889	+3.2647%	+15.7690	+3.0345%	+3.0345%

Known prime factors (1 factor, 81.2 bits, 0.00212591% 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
3817783	2706182010504192221411593	25	81.163	354417997369702812 2² × 3 × 7 × 13 × 1151 × 281979674761	2017-08-30	1151	281979674761	181,920	2,339.6	4,369.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-24T04:43:00	Carsten Kossendey	leela	20000	270000		-		-	-	0.005	-	-	0.999%
2011-11-02T22:13:00	Squeeky_Squirrel	T7500_2200	65000	1121250		-		-	-	0.019	-	-	2.050%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	81812	81812		-		-	-	0.012	-	-	0.790%
2016-01-31T15:29:04	Jocelyn Larouche	Manual testing	258724	2587240	6	-		-	-	0.059	-	-	3.190%
2016-01-31T15:29:07	Jocelyn Larouche	Manual testing	310468	3104680	6	-		-	-	0.070	-	-	3.409%
2022-03-05T00:34:48	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.836%
2022-03-22T17:33:31	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.890%
2022-05-24T23:56:34	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	5.430%

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	-	-
2009-02-26T08:00:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.040	-	-
2011-03-14T12:15:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.080	-	-
2012-03-23T23:24:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.418	-	-
2016-02-23T16:29:40	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.257	-	-
2015-01-18T20:59:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.514	-	-
2015-01-18T20:59:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.979	-	-
2016-02-26T10:03:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.957	-	-
2016-11-17T14:52:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.915	-	-
2022-03-22T17:39:49	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	7.829	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.800 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%

New Calculation Method

Total ECM effort:	1.800 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.350
50000	5000000	2706182010504192221411593	3	0.450

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-20T02:39:00	S36049	Wolle2	50000	5000000						3	0.450
2012-09-02T05:53:00	driveByUpgrades		50000	5000000						3	0.450
2016-01-22T01:51:16	driveByUpgrades	Build_4	50000	5000000						3	0.450
2017-08-30T16:36:22	Bruce	desk	50000	5000000	2706182010504192221411593	81.163	3	2		3	0.450

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-07T00:00:00	ANONYMOUS	v4_computers	9CF6BF73C02A49E1	0.401

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:10:10

alpertron

Manual testing

2706182010504192221411593

772AE14C491398__

2017-12-11T20:43:31

kkmrkkblmbrbk

c4.xlarge

2706182010504192221411593

772AE14C491398__

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

B1 = 310468, B2 = 3104680 (P-1 stage 2)

B1 = 258724, B2 = 2587240 (P-1 stage 2)

B1 = 310468 (P-1 stage 1)

B1 = 258724 (P-1 stage 1)

B1 = 65000, B2 = 1121250 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 81812 (P-1 stage 1)

B1 = 65000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-24T23:56:34+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