M3482021 Mersenne number exponent details

≡

M3482021

<<<

>>>

is 2 ^3482021 - 1

has 1048193 decimal digits

takes 0.366 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	D22D8704214C0278	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	17.1179	67.6471%	1096404	114656850	1.1092	7.5996%	18.2271	70.1058%	2.4587%
PrimeNet	2⁶⁰	0.0441	63.3333%	15000	300000	0.0046	2.9578%	0.0488	64.4178%	1.0845%
GPU72	2⁶⁴	1.0222	65.6250%	19000	360000	0.0057	1.8870%	1.0279	66.2737%	0.6487%
Difference	+4	+16.0957	+2.0221%	+1077404	+114296850	+1.1035	+5.7127%	+17.1992	+3.8321%	+3.8321%

Known prime factors (1 factor, 80.5 bits, 0.00231162% 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
3482021	1699184410843978033542569	25	80.491	243993992403259204 2² × 17 × 3588146947106753	2017-01-13	17	3588146947106753	135,227	29,771,553	55,604,970

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2014-09-28T15:46:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.598%
2021-02-18T11:47:31	Jocelyn Larouche	Manual testing	348202	3830223	6	-		-	-	0.082	-	-	3.586%
2022-01-25T03:35:34	Jocelyn Larouche	Manual testing	1096404	114656850		-		-	-	1.109	-	-	7.600%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:31	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.088	-	-
2011-07-19T07:11:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.088	-	-
2012-08-18T15:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.458	-	-
2016-02-23T16:29:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.282	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.564	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.073	-	-
2021-02-24T21:45:56	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.146	-	-
2016-01-05T09:38:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.146	-	-
2022-06-03T00:52:08	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.292	-	-
2021-06-13T12:36:30	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.584	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.620 GHz-days
Estimated T-Level:	0.550

Digits	B1	Curves	Complete	FacMiss
20	11000	11 / 100	0.110	89.534%
25	50000	11 / 280	0.039	96.141%

New Calculation Method

Total ECM effort:	1.620 GHz-days
Estimated T-Level:	0.550

Digits	B1	Complete	FacMiss
20	11000	0.423	65.503%
25	50000	0.039	96.161%
30	250000	0.002	99.753%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.325
50000	5000000	1699184410843978033542569	2	0.295

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-05T15:24:00	Smurgs	Praca	50000	5000000						3	0.442
2012-02-26T18:21:00	oodaira	Linux01	50000	5000000						3	0.442
2015-03-31T06:08:00	Bruce	agent86	50000	5000000						3	0.442
2017-01-13T23:50:49	Sid & Andy	Mrs_Potato_Head	50000	5000000	1699184410843978033542569	80.491	2	2		2	0.295

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-07T00:00:00	lozcs	v4_computers	D22D8704214C0278	0.366
2000-03-08T00:00:00	lozcs	v4_computers	D22D8704214C0278	0.366

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-06T23:33:54

kkmrkkblmbrbk

c4.xlarge

1699184410843978033542569

774D720BEE3D8B__

2017-11-23T16:21:44

Oliver Kruse

GTX-1

1699184410843978033542569

774D720BEE3D8B__

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 = 1096404, B2 = 114656850 (P-1 stage 2)

B1 = 1096404 (P-1 stage 1)

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

B1 = 348202, B2 = 3830223 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 348202 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-06-03T00:52:08+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