M3468293 Mersenne number exponent details

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M3468293

<<<

>>>

is 2 ^3468293 - 1

has 1044061 decimal digits

takes 0.364 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	0AACF1BA16C0AE6C	double-checked
PRP	88089BC063B7C1F6	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	34.4223	68.1159%	20000000	1000000000	11.1771	11.6166%	45.5994	71.8198%	3.7038%
PrimeNet	2⁶⁰	0.0443	63.3333%	15000	280000	0.0045	2.9041%	0.0488	64.3982%	1.0648%
GPU72	2⁶⁴	1.0262	65.6250%	19000	360000	0.0057	1.8856%	1.0320	66.2732%	0.6482%
Difference	+5	+33.3961	+2.4909%	+19981000	+999640000	+11.1713	+9.7310%	+44.5674	+5.5466%	+5.5466%

Known prime factors (1 factor, 92.8 bits, 0.00267444% 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
3468293	8369981179417143235425196079	28	92.757	1206642746073809686123 12269 × 26573 × 3701084088979	2021-10-27	26573	3701084088979	382,010,550	30,709	57,355

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:18:00	Carsten Kossendey	leela	20000	235000		-		-	-	0.005	-	-	0.806%
2011-11-10T05:57:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.688%
2014-07-28T22:42:00	Jocelyn Larouche	Manual testing	78506	78506		-		-	-	0.012	-	-	0.653%
2014-09-24T22:36:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.165%
2021-03-30T02:08:46	axn	Manual testing	20000000	1000000000		-		-	-	11.18	-	-	11.617%
2022-04-10T23:56:43	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.999%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-23T00:00:00	Trent Taufer	v4_computers	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-21T17:05:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-23T10:53:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.089	-	-
2012-08-18T15:35:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.460	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.283	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.566	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.077	-	-
2016-01-04T09:40:09	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.155	-	-
2017-02-10T15:33:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.309	-	-
2019-01-28T14:25:39	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.618	-	-
2021-01-08T11:31:09	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.24	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.799 GHz-days
Estimated T-Level:	2.650

Digits	B1	Curves	Complete	FacMiss
20	11000	53 / 100	0.530	58.704%
25	50000	53 / 280	0.189	82.727%

New Calculation Method

Total ECM effort:	7.799 GHz-days
Estimated T-Level:	2.650

Digits	B1	Complete	FacMiss
20	11000	1.710	18.092%
25	50000	0.155	85.683%
30	250000	0.010	99.053%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	6.327
50000	5000000	8369981179417143235425196079	10	1.471

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-18T12:05:00	Aca Arsov	backo6400	50000	5000000						3	0.441
2012-02-15T21:08:00	Smurgs	Praca	50000	5000000						3	0.441
2015-03-11T13:15:00	driveByUpgrades	Build_4	50000	5000000						3	0.441
2016-12-30T09:32:40	Bruce	agent86	50000	5000000						3	0.441
2019-06-20T21:19:23	IanGlencross	glenx24	50000	5000000						3	0.441
2021-04-01T11:09:10	mnd9	l2lounge	50000	5000000						7	1.030
2021-05-31T06:39:24	C.D.B.	i7-6850K	50000	5000000						7	1.030
2021-07-02T08:52:30	Jonathan Webb	do-primes-2	50000	5000000						7	1.030
2021-08-17T21:08:49	daveward2005	Dave2	50000	5000000						7	1.030
2021-10-27T08:59:17	MarkS	desktop-i7	50000	5000000	8369981179417143235425196079	92.757	10	2	1435485868418128	10	1.471

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-01T00:00:00	ANONYMOUS	v4_computers	0AACF1BA16C0AE6C	0.364
1999-12-15T00:00:00	ANONYMOUS	v4_computers	0AACF1BA16C0AE6C	0.364
2000-02-01T00:00:00	ANONYMOUS	v4_computers	0AACF1BA16C0AE6C	0.364

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-27T13:29:08

MarkS

desktop-i7

8369981179417143235425196079

88089BC063B7C1F6

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 = 20000000, B2 = 1000000000 (P-1 stage 2)

B1 = 20000000 (P-1 stage 1)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

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

B1 = 78506 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 235000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T23:56:43+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