M3385747 Mersenne number exponent details

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M3385747

<<<

>>>

is 2 ^3385747 - 1

has 1019212 decimal digits

takes 0.356 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

1 primality tests remaining

	Residue	Status
L-L	D8C72DE7DF020A4B	double-checked
PRP	34A01C487B5734__	unverified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	17.6046	67.6471%	4000000	150000000	1.8206	8.8077%	19.4252	70.4966%	2.8495%
PrimeNet	2⁶⁰	0.0454	63.3333%	14000	280000	0.0043	2.8451%	0.0497	64.3765%	1.0432%
GPU72	2⁶⁴	1.0513	65.6250%	18000	320000	0.0052	1.7906%	1.0565	66.2405%	0.6155%
Difference	+4	+16.5534	+2.0221%	+3982000	+149680000	+1.8153	+7.0171%	+18.3687	+4.2561%	+4.2561%

Known prime factors (1 factor, 93.1 bits, 0.00274835% 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
3385747	10267651243418758150929326441	29	93.052	1516305152661843627260 2² × 5 × 1151 × 2287 × 2494463 × 11546173	2021-05-28	2494463	11546173	802,781,939	0.4550	0.7731

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-10T06:11:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.811%
2011-10-21T19:05:00	harlee	P4_2600	60000	930000		-		-	-	0.016	-	-	1.881%
2014-07-04T02:22:00	Jocelyn Larouche	Manual testing	78957	78957		-		-	-	0.012	-	-	0.755%
2014-10-13T22:29:00	Jocelyn Larouche	Manual testing	97914	97914		-		-	-	0.015	-	-	0.859%
2015-09-20T21:18:00	Squeeky_Squirrel	P4_2600	155000	4030000		-		-	-	0.056	-	-	3.217%
2017-03-31T00:48:08	Jocelyn Larouche	low 4M	310000	3100000	6	-		-	-	0.070	-	-	3.353%
2021-05-28T07:23:03	mikr	MSI	4000000	150000000	12		10267651243418758150929326441	29	93.052	1.821	0.711	3.641	8.808%
2022-02-25T17:22:03	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.030	-	-	1.270%
2022-04-09T09:24:11	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.570%
2022-04-10T15:21:20	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	7.612%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-25T20:44:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-09-12T03:12:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.091	-	-
2012-11-15T00:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.471	-	-
2016-02-23T16:29:27	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.290	-	-
2015-02-15T12:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.580	-	-
2015-02-15T12:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.104	-	-
2015-04-02T13:03:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.207	-	-
2017-03-10T14:13:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.414	-	-
2018-10-01T11:53:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.828	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.273 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	5.273 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.273

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-11T23:24:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.439
2011-12-17T02:48:00	sannerud.com	Jens2010	50000	5000000						3	0.439
2014-10-25T00:14:00	joe b.	Pandora	50000	5000000						3	0.439
2016-11-15T13:16:51	Dennis Schreiber	z400	50000	5000000						3	0.439
2019-04-22T19:33:50	nranks	wlaptop	50000	5000000						3	0.439
2021-02-25T17:07:16	IanGlencross	glenx24	50000	5000000						7	1.025
2021-03-31T03:11:50	mnd9	50871	50000	5000000						7	1.025
2021-05-22T14:48:40	Stefan G. Hoffmann	PC-HRW-EILab-5	50000	5000000						7	1.025

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-09-06T00:00:00	ANONYMOUS	v4_computers	D8C72DE7DF020A4B	0.356
1999-07-12T00:00:00	MadPoo	v4_computers	D8C72DE7DF020A4B	0.356

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-30T09:40:21

A child prodigy in maths

math_child_prodigy

10267651243418758150929326441

34A01C487B5734__

2021-07-01T22:07:16

marssystems

system11

10267651243418758150929326441

34A01C487B57340E

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 = 126668850 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 310000, B2 = 3100000 (P-1 stage 2)

B1 = 155000, B2 = 4030000 (P-1 stage 2)

B1 = 310000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 155000 (P-1 stage 1)

B1 = 60000, B2 = 930000 (P-1 stage 2)

B1 = 97914 (P-1 stage 1)

B1 = 78957 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T15:21:20+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