M3138589 Mersenne number exponent details

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M3138589

<<<

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is 2 ^3138589 - 1

has 944810 decimal digits

takes 0.267 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	1C6184E2CE5F1086	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	2⁶⁸	18.9910	67.6471%	3000000	100000000	1.0224	8.0577%	20.0134	70.2540%	2.6069%
PrimeNet	2⁶⁰	0.0489	63.3333%	13000	240000	0.0031	2.6481%	0.0521	64.3043%	0.9710%
GPU72	2⁶⁴	1.1341	65.6250%	15000	240000	0.0034	1.5431%	1.1374	66.1555%	0.5305%
Difference	+4	+17.8569	+2.0221%	+2985000	+99760000	+1.0191	+6.5146%	+18.8760	+4.0985%	+4.0985%

Known prime factors (1 factor, 87.1 bits, 0.00277498% 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
3138589	165287492046797775022737961	27	87.095	26331496740541334820 2² × 3 × 5 × 438858279009022247	2021-03-25	5	438858279009022247	18,675,708	2.951e+9	5.511e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.251%
2009-07-03T00:57:00	Carsten Kossendey	leela	15000	183750		-		-	-	0.003	-	-	0.769%
2011-11-02T23:05:00	markr	tiny	210000	5460000		-		-	-	0.061	-	-	3.569%
2018-08-06T19:37:33	Jocelyn Larouche	low 4M	420000	840000		-		-	-	0.055	-	-	2.345%
2018-08-07T17:09:34	Jocelyn Larouche	low 4M	420000	1260000		-		-	-	0.057	-	-	2.678%
2018-08-13T19:32:42	Jocelyn Larouche	low 4M	420000	3360000		-		-	-	0.072	-	-	3.502%
2018-08-14T23:01:50	Jocelyn Larouche	low 4M	420000	3780000		-		-	-	0.074	-	-	3.602%
2019-02-08T17:08:42	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.058%
2022-01-24T00:01:35	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	7.491%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-12T16:31:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-10T10:12:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.098	-	-
2013-01-03T08:44:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.313	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.626	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.190	-	-
2015-06-14T13:51:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.381	-	-
2017-04-17T17:51:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.762	-	-
2019-01-07T14:44:23	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.52	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.502 GHz-days
Estimated T-Level:	2.350

Digits	B1	Curves	Complete	FacMiss
20	11000	47 / 100	0.470	62.353%
25	50000	47 / 280	0.168	84.522%

New Calculation Method

Total ECM effort:	5.502 GHz-days
Estimated T-Level:	2.350

Digits	B1	Complete	FacMiss
20	11000	1.808	16.403%
25	50000	0.167	84.598%
30	250000	0.011	98.951%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	5.033
50000	5000000	165287492046797775022737961	4	0.468

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-29T23:34:00	Martti Järvi	Mardeni	50000	5000000						3	0.351
2011-11-02T13:52:00	S00030	op9020-usff	50000	5000000						3	0.351
2014-02-04T01:48:00	Richard Kint	Desktop	50000	5000000						3	0.351
2016-06-09T14:43:27	Bruce	agent86	50000	5000000						3	0.351
2018-03-27T02:43:46	Aare Vesi	h1	50000	5000000						3	0.351
2020-11-16T19:17:56	MarkS	desktop-i7	50000	5000000						7	0.819
2020-12-24T04:55:01	Zenzoma	AMD3970X	50000	5000000						7	0.819
2021-01-28T04:14:48	arachnotron	AsusLaptop	50000	5000000						7	0.819
2021-02-22T08:30:14	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.819
2021-03-25T20:42:37	Zenzoma	AM3700X_1	50000	5000000	165287492046797775022737961	87.095	4	2	4512825926544464	4	0.468

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	D30D22ABCCC9CE__	0.267

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-01T14:30:19

Chang Chia-Tche

exbpc13

165287492046797775022737961

1C6184E2CE5F1086

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 420000, B2 = 3780000 (P-1 stage 2)

B1 = 420000, B2 = 3360000 (P-1 stage 2)

B1 = 210000, B2 = 5460000 (P-1 stage 2)

B1 = 420000, B2 = 1260000 (P-1 stage 2)

B1 = 420000, B2 = 840000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 210000 (P-1 stage 1)

B1 = 15000, B2 = 183750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

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10²

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10⁴

10⁵

10⁶

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10¹⁰

10¹¹

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-24T00:01:35+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