M3558671 Mersenne number exponent details

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M3558671

<<<

>>>

is 2 ^3558671 - 1

has 1071267 decimal digits

takes 0.374 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	-unknown-	-unknown-
PRP	4ED255849054ADE7	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	2⁷¹	134.3418	69.0141%	350000	3500000	0.0794	2.5605%	134.4212	69.8075%	0.7934%
PrimeNet	2⁶⁰	0.0432	63.3333%	15000	300000	0.0046	2.9691%	0.0478	64.4220%	1.0887%
GPU72	2⁶⁴	1.0002	65.6250%	20000	360000	0.0059	1.9212%	1.0061	66.2854%	0.6604%
Difference	+7	+133.3416	+3.3891%	+330000	+3140000	+0.0736	+0.6393%	+133.4152	+3.5221%	+3.5221%

Known prime factors (1 factor, 74.8 bits, 0.00210326% 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
3558671	34000193300848622302759	23	74.848	4777091405871549 3 × 6653 × 239345228011	2021-07-06	6653	239345228011	1,468.1	1,985.9	3,709.1

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T17:51:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.603%
2011-12-17T21:37:00	Squeeky_Squirrel	P4_2600	60000	1005000		-		-	-	0.017	-	-	1.308%
2014-08-11T01:34:00	ANONYMOUS	Manual testing	78036	78036		-		-	-	0.012	-	-	0.485%
2014-11-19T23:20:00	Jocelyn Larouche	Manual testing	96072	96072		-		-	-	0.015	-	-	0.556%
2015-12-25T19:49:27	Squeeky_Squirrel	P4_2600	175000	4681250	6	-		-	-	0.064	-	-	2.444%
2017-05-06T16:05:26	Jocelyn Larouche	low 4M	350000	3500000	6	-		-	-	0.079	-	-	2.560%
2022-03-01T15:49:51	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.570%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:33	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.043	-	-
2009-03-16T06:10:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.043	-	-
2011-06-25T06:14:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.086	-	-
2012-06-20T01:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.448	-	-
2016-02-23T16:29:33	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.276	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.552	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.050	-	-
2016-03-03T09:33:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.100	-	-
2017-01-16T05:00:24	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.200	-	-
2019-02-04T14:28:15	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.399	-	-
2021-01-26T02:10:46	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.80	-	-
2021-03-18T11:36:31	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	33.60	-	-
2021-03-18T11:36:31	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	67.20	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.289 GHz-days
Estimated T-Level:	1.450

Digits	B1	Curves	Complete	FacMiss
20	11000	29 / 100	0.290	74.717%
25	50000	29 / 280	0.104	90.144%

New Calculation Method

Total ECM effort:	4.289 GHz-days
Estimated T-Level:	1.450

Digits	B1	Complete	FacMiss
20	11000	0.935	39.240%
25	50000	0.085	91.893%
30	250000	0.005	99.481%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.254
50000	5000000	34000193300848622302759	7	1.035

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-01-27T09:48:00	James Heinrich	WHS	50000	5000000						3	0.444
2012-04-12T01:54:00	Lukasz Wrobel	i-5	50000	5000000						3	0.444
2015-06-15T14:17:00	joe b.	Pandora	50000	5000000						3	0.444
2017-03-17T07:46:04	bayanne	iMac	50000	5000000						3	0.444
2019-11-10T15:25:24	mnd9	75204	50000	5000000						3	0.444
2021-05-31T03:52:37	GAN	KL-SCH01	50000	5000000						7	1.035
2021-07-06T15:30:55	daveward2005	d12436	50000	5000000	34000193300848622302759	74.848	7	2	1228291871951590	7	1.035

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	ANONYMOUS	v4_computers	8499A512B4A4BC__	0.374

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-07-07T15:32:06

SRJ2877

LTOS

34000193300848622302759

4ED255849054ADE7

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 = 350000, B2 = 3500000 (P-1 stage 2)

B1 = 175000, B2 = 4681250 (P-1 stage 2)

B1 = 350000 (P-1 stage 1)

B1 = 175000 (P-1 stage 1)

B1 = 60000, B2 = 1005000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 96072 (P-1 stage 1)

B1 = 78036 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 245000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-01T15:49:51+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