M3174337 Mersenne number exponent details

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M3,174,337

<<<

>>>

is 2^3174337-1

has 955,571 decimal digits

takes 0.270 GHz-days to do one L-L test

Last-known PrimeNet details:
0 L-L tests remaining

	Residue	Status
L-L	EDC601E5159D4B63	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	18.7771	67.6471%	3,000,000	120,000,000	1.1569	8.2951%	19.9340	75.9421%	12.6088%
PrimeNet	2⁶⁰	0.0484	63.3333%	13,000	240,000	0.0031	2.6536%	0.0515	65.9869%	2.6536%
GPU72	2⁶⁴	1.1213	65.6250%	15,000	260,000	0.0035	1.5823%	1.1248	67.2073%	1.5823%
Difference	+4	+17.6558	+2.0221%	+2,985,000	+119,740,000	+1.1534	+6.7127%	+18.8092	+8.7348%	+8.7348%

Known prime factors (1 factor, 127.0 bits, 0.00400175% known):

Remaining cofactor is not a probable-prime

								GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
3174337	173602443592748619932666102019626694673	39	127.029	27344677580349632054294503390728 2³ × 3 × 7 × 17 × 89 × 1319 × 96001 × 201211 × 875327 × 4823719	875,327	4,823,719	2019-08-28	5.772e+10	0.1346	0.2198

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-16T00:00:00	ANONYMOUS	v4_computers	2,048	204,800		-		-	-	0.002	-	-	0.252%
2003-02-24T00:00:00	ANONYMOUS	v4_computers	4,096	409,600		-		-	-	0.003	-	-	0.509%
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2,048	204,800		-		-	-	0.002	-	-	0.252%
2017-01-30T01:30:34	Jocelyn Larouche low 4M	Manual testing	157,286	157,286		-		-	-	0.019	-	-	1.108%
2017-02-04T18:42:42	Jocelyn Larouche low 4M	Manual testing	188,743	188,743		-		-	-	0.023	-	-	1.219%
2017-03-15T21:59:27	Jocelyn Larouche low 4M	Manual testing	262,144	2,621,440	6	-		-	-	0.048	-	-	3.126%
2017-03-17T00:42:28	Jocelyn Larouche low 4M	Manual testing	314,572	3,145,720	6	-		-	-	0.058	-	-	3.341%
2017-03-19T01:08:41	Jocelyn Larouche low 4M	Manual testing	377,486	3,774,860	6	-		-	-	0.069	-	-	3.564%
2017-03-20T00:25:08	Jocelyn Larouche low 4M	Manual testing	452,983	4,529,830	6	-		-	-	0.083	-	-	3.794%
2017-03-21T02:10:23	Jocelyn Larouche low 4M	Manual testing	543,579	5,435,790	6	-		-	-	0.100	-	-	4.031%
2017-03-24T21:04:51	Jocelyn Larouche low 4M	Manual testing	652,294	6,522,940	6	-		-	-	0.120	-	-	4.274%
2019-08-28T06:34:09	mikr	MSI	3,000,000	120,000,000	12		173602443592748619932666102019626694673	39	127.029	1.157	0.540	2.314	8.295%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁹		-	-	0.012	-	-
1998-08-16T00:00:00	ANONYMOUS	v4_computers	?	2⁶⁰		-	-	0.024	-	-
2009-04-10T08:17:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-24T00:25:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.097	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.309	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.618	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.177	-	-
2015-06-17T22:19:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.354	-	-
2017-04-25T10:21:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.708	-	-
2019-01-07T14:44:21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.416	-	-

ECM factoring results:

ECM Summary

B1	B2	factor	curves	GHz-days
33,334	4,000,000		2	0.170
50,000	5,000,000		15	1.759

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-06T14:43:00	Net_Force	Vista64	50,000	5,000,000						3	0.352
2011-02-12T01:47:00	Oscar Östlin		33,334	4,000,000						2	0.170
2012-10-21T00:53:00	Donna Noble	i3-2100t	50,000	5,000,000						3	0.352
2015-07-03T04:27:00	KAMCOBILL	PC20	50,000	5,000,000						3	0.352
2016-09-08T10:57:35	Bruce	test	50,000	5,000,000						3	0.352
2019-06-25T03:31:11	IanGlencross	glenx24	50,000	5,000,000						3	0.352

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-18T00:00:00	ANONYMOUS	v4_computers	EDC601E5159D4B63	0.270

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-08-29T13:55:38

mnd9

office

173602443592748619932666102019626694673

53F3343D232B6279

2019-08-29T15:26:46

ATH

ec2-PRPCFDC

173602443592748619932666102019626694673

53F3343D232B6279

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 = 3,000,000, B2 = 120,000,000 (stage 2)

B1 = 3,000,000 (stage 1)

B1 = 652,294, B2 = 6,522,940 (stage 2)

B1 = 543,579, B2 = 5,435,790 (stage 2)

B1 = 452,983, B2 = 4,529,830 (stage 2)

B1 = 652,294 (stage 1)

B1 = 377,486, B2 = 3,774,860 (stage 2)

B1 = 543,579 (stage 1)

B1 = 314,572, B2 = 3,145,720 (stage 2)

B1 = 452,983 (stage 1)

B1 = 262,144, B2 = 2,621,440 (stage 2)

B1 = 377,486 (stage 1)

B1 = 314,572 (stage 1)

B1 = 262,144 (stage 1)

B1 = 188,743 (stage 1)

B1 = 157,286 (stage 1)

B1 = 4,096, B2 = 409,600 (stage 2)

B1 = 2,048, B2 = 204,800 (stage 2)

B1 = 4,096 (stage 1)

B1 = 2,048 (stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2019-08-29T15:26:46+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	<	123M	PrimeNet wavefront