M3392953 Mersenne number exponent details

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M3392953

<<<

>>>

is 2 ^3392953 - 1

has 1021381 decimal digits

takes 0.356 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	BBE258852BF38F67	double-checked
PRP	846A2F309854B8E2	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	70.4256	68.5714%	4000000	150000000	1.8206	7.5198%	72.2461	70.9348%	2.3634%
PrimeNet	2⁶⁰	0.0453	63.3333%	14000	280000	0.0043	2.8462%	0.0496	64.3769%	1.0436%
GPU72	2⁶⁴	1.0490	65.6250%	18000	320000	0.0052	1.7913%	1.0543	66.2408%	0.6158%
Difference	+6	+69.3765	+2.9464%	+3982000	+149680000	+1.8153	+5.7285%	+71.1918	+4.6940%	+4.6940%

Known prime factors (1 factor, 72.9 bits, 0.00214845% 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
3392953	8787847231875905858657	22	72.896	1295014583443376 2⁴ × 80938411465211	2021-08-29	16	80938411465211	424.40	671,562	1,254,290

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-10T14:36:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.590%
2011-10-23T10:01:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.457%
2014-07-04T02:22:00	Jocelyn Larouche	Manual testing	78917	78917		-		-	-	0.012	-	-	0.562%
2014-10-13T22:29:00	Jocelyn Larouche	Manual testing	97834	97834		-		-	-	0.015	-	-	0.645%
2015-10-27T22:07:21	Squeeky_Squirrel	P4_2600	165000	4372500	6	-		-	-	0.060	-	-	2.648%
2016-07-23T03:35:16	Jocelyn Larouche	Manual testing	302354	8745000	6	-		-	-	0.116	-	-	3.405%
2021-06-06T07:51:00	mognuts	Manual testing	1000000	30000000		-		-	-	0.393	-	-	5.052%
2021-07-07T04:52:16	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	7.520%
2022-04-06T23:14:02	Jocelyn Larouche	Manual testing	1000000	123342450		-		-	-	1.167	-	-	6.371%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-25T20:45:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-19T23:18:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.091	-	-
2012-11-15T00:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.470	-	-
2016-02-23T16:29:27	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.289	-	-
2015-02-18T11:36:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.579	-	-
2015-02-18T11:36:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.101	-	-
2015-04-04T13:44:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.202	-	-
2017-03-12T14:28:48	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.405	-	-
2018-09-17T14:42:51	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.810	-	-
2021-06-28T11:10:42	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	17.62	-	-
2021-08-28T02:07:14	MadPoo	Manual testing	2⁶⁹	2⁷⁰		-	-	35.24	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.959 GHz-days
Estimated T-Level:	3.000

Digits	B1	Curves	Complete	FacMiss
20	11000	60 / 100	0.600	54.716%
25	50000	60 / 280	0.214	80.681%

New Calculation Method

Total ECM effort:	8.959 GHz-days
Estimated T-Level:	3.000

Digits	B1	Complete	FacMiss
20	11000	1.960	14.090%
25	50000	0.177	83.806%
30	250000	0.011	98.917%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.275
50000	5000000	8787847231875905858657	17	2.491
50000	6800000		7	1.192

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-13T06:44:00	rextherunt	ccrc468-3	50000	5000000						3	0.440
2011-12-20T07:57:00	Smurgs	Praca	50000	5000000						3	0.440
2014-11-07T00:49:00	S36049	Wolle6	50000	5000000						3	0.440
2016-11-19T20:36:07	Dennis Schreiber	z400	50000	5000000						3	0.440
2019-04-27T15:53:59	nokno	leo235	50000	5000000						3	0.440
2021-02-28T00:07:06	Zenzoma	AMD3970X	50000	5000000						7	1.026
2021-04-03T15:53:44	Zenzoma	AM3700X_1	50000	5000000						7	1.026
2021-05-26T12:02:39	daveward2005	d12436	50000	5000000						7	1.026
2021-07-04T02:02:52	Dylan Delgado	colab	50000	6800000						7	1.192
2021-08-29T02:00:58	MarkS	desktop-i7	50000	5000000	8787847231875905858657	72.896	17	2	4811105621113814	17	2.491

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-04-05T00:00:00	ANONYMOUS	v4_computers	BBE258852BF38F67	0.356
1999-09-14T00:00:00	ANONYMOUS	v4_computers	BBE258852BF38F67	0.356

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-29T07:17:00

SRJ2877

LTOS

8787847231875905858657

846A2F309854B8E2

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 = 123342450 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 302354, B2 = 8745000 (P-1 stage 2)

B1 = 165000, B2 = 4372500 (P-1 stage 2)

B1 = 302354 (P-1 stage 1)

B1 = 165000 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 97834 (P-1 stage 1)

B1 = 78917 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

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10²

10³

10⁴

10⁵

10⁶

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10¹⁰

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TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-06T23:14:02+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