M3 492 457 Mersenne number exponent details

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M3492457

<<<

>>>

is 2 ^3492457 - 1

has 1051335 decimal digits

takes 0.367 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	6BBFE5193BBF3D1A	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁰	68.4191	68.5714%	14000000	700000000	7.8239	10.1932%	76.2430	71.7750%
Target	2⁶⁴	1.0191	65.6250%	19000	1800000	0.0177	1.8880%	1.0368	66.2740%
Difference	+6	+67.3999	+2.9464%	+13981000	+698200000	+7.8063	+8.3052%	+75.2062	+5.5010%

Known prime factors (1 factor, 76.1 bits, 0.00217945% 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
3492457	81901143604554300134137	23	76.116	11725433356023324 2² × 3² × 7 × 36691 × 1268144707	2023-08-30	36691	1268144707	8,047.0	10.527	19.652

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-08	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.697%
2011-11-17	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.482%
2014-08-21	Jocelyn Larouche	Manual testing	78378	78378		-		-	-	0.012	-	-	0.563%
2014-09-05	HBendtz	Manual testing	615000	12000000		-		-	-	0.188	-	-	4.020%
2021-04-18	axn	Manual testing	14000000	700000000		-		-	-	7.824	-	-	10.193%
2023-08-30	Joss	Joss	1000000	1508917410			81901143604554300134137	23	76.116	12.66	0.734	25.33	8.850%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	Stephen Wood	v4_computers	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-19	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-17	markr	Manual testing	2¹	2⁶²		-	-	0.176	-	-
2012-08-18	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.457	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.281	-	-
2015-02-07	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.562	-	-
2015-02-07	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.070	-	-
2016-01-06	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.140	-	-
2017-02-20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.279	-	-
2018-08-20	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.559	-	-
2021-01-13	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.12	-	-
2022-02-16	TJAOI	Manual testing	2⁶⁹	2⁷⁰		-	-	34.23	-	-

ECM factoring results:

Total ECM effort:	11.928 GHz-days
Estimated T-Level:	21.398

Digits	B1	Complete	FacMiss
20	11000	3.017	4.894%
25	50000	0.280	75.610%
30	250000	0.018	98.246%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	43	6.336
50000	6135885	7	1.138
50000	6609634	5	0.845
50000	6800000	14	2.400
50000	6900000	7	1.210

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-21	Aca Arsov	backo6400	50000	5000000						3	0.442
2012-03-08	Smurgs	Praca	50000	5000000						3	0.442
2015-04-12	Bruce	S2600KP	50000	5000000						3	0.442
2017-01-17	Dennis Schreiber	z400	50000	5000000						3	0.442
2019-07-18	Per Jessen	earth	50000	5000000						3	0.442
2021-04-16	Zenzoma	AMD3970X	50000	5000000						7	1.031
2021-06-08	Dylan Delgado	colab	50000	6800000						7	1.200
2021-07-25	kutens	arcturus	50000	6800000						7	1.200
2021-09-30	Kamil Mudrunka	LinuxServer	50000	5000000						7	1.031
2022-01-01	RIHATEC	i7-3770K	50000	5000000						7	1.031
2022-04-19	J.R. Allen	lapasus	50000	6135885						7	1.138
2022-07-26	RIHATEC	i7-3770K	50000	5000000						7	1.031
2022-10-23	Alvin Bunk	BADCAT	50000	6900000						7	1.210
2023-02-09	COMPUTRON9001	BOBO	50000	6609634						5	0.845

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-08-16	Stephen Wood	v4_computers	6BBFE5193BBF3D1A	0.367
1999-09-30	ANONYMOUS	v4_computers	6BBFE5193BBF3D1A	0.367

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-08-30

Naegi Makoto

12500H

81901143604554300134137

546FA19E8470A558

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 = 1000000, B2 = 1508917410 (P-1 stage 2)

B1 = 14000000, B2 = 700000000 (P-1 stage 2)

B1 = 14000000 (P-1 stage 1)

B1 = 615000, B2 = 12000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 615000 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 78378 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (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:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

this exponent TF target: 64

TF double-checked to: 67.9

ECM T-Level=21.4 ~= 54-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+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