M3082127 Mersenne number exponent details

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M3082127

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>>>

is 2 ^3082127 - 1

has 927813 decimal digits

takes 0.262 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	0C03CF544771E22B	double-checked
PRP	8E0895D0951B1F__	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	2⁶⁹	38.7352	68.1159%	3000000	100000000	1.0224	7.4138%	39.7576	70.4798%	2.3638%
PrimeNet	2⁶⁰	0.0498	63.3333%	12000	220000	0.0029	2.5277%	0.0527	64.2601%	0.9268%
GPU72	2⁶⁴	1.1548	65.6250%	14000	220000	0.0031	1.4680%	1.1579	66.1296%	0.5046%
Difference	+5	+37.5804	+2.4909%	+2986000	+99780000	+1.0193	+5.9459%	+38.5997	+4.3502%	+4.3502%

Known prime factors (1 factor, 89.4 bits, 0.00290161% 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
3082127	834675688858144084964823191	27	89.431	135405791010257540485 5 × 461 × 58744377878636677	2021-03-31	461	58744377878636677	57,801,882	394,984,143	737,720,383

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.201%
2010-09-17T16:09:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.193%
2016-04-12T21:52:05	Jocelyn Larouche	Manual testing	190000	5880973	6	-		-	-	0.062	-	-	3.192%
2016-04-13T19:08:28	harlee	P4_2600	210000	5985000	12	-		-	-	0.065	-	-	3.259%
2018-03-16T11:31:21	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.414%
2022-02-20T22:18:07	Jocelyn Larouche	Manual testing	1000000	128282700		-		-	-	0.979	-	-	6.923%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
1998-07-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
2001-07-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-14T09:56:00	Sturle Sunde	herrick.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-11-11T22:43:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.100	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.318	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.637	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.212	-	-
2015-06-08T12:39:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.425	-	-
2017-05-18T12:32:20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.849	-	-
2022-01-20T22:38:01	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.70	-	-
2018-08-10T10:59:49	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.70	-	-
2021-03-10T09:10:09	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.534 GHz-days
Estimated T-Level:	2.800

Digits	B1	Curves	Complete	FacMiss
20	11000	56 / 100	0.560	56.960%
25	50000	56 / 280	0.200	81.844%

New Calculation Method

Total ECM effort:	6.534 GHz-days
Estimated T-Level:	2.800

Digits	B1	Complete	FacMiss
20	11000	1.806	16.424%
25	50000	0.163	84.937%
30	250000	0.010	99.000%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		50	5.834
50000	5000000	834675688858144084964823191	6	0.700

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-20T03:58:00	oodaira	Win02	50000	5000000						3	0.350
2011-07-19T02:11:00	Smurgs	Praca	50000	5000000						3	0.350
2013-11-06T20:54:00	Richard Kint	xps	50000	5000000						3	0.350
2016-07-09T02:12:16	Lelikoid	QH	50000	5000000						3	0.350
2017-10-10T14:40:19	bayanne	iMac	50000	5000000						3	0.350
2020-10-18T18:27:01	rextherunt	ice	50000	5000000						7	0.817
2020-11-19T09:24:41	daveward2005	Dave2	50000	5000000						7	0.817
2020-12-26T07:14:17	Zenzoma	AMD3970X	50000	5000000						7	0.817
2021-01-26T17:02:51	Zenzoma	AMD3970X	50000	5000000						7	0.817
2021-02-25T05:04:19	Zenzoma	AMD3970X	50000	5000000						7	0.817
2021-03-31T00:14:41	mnd9	75204	50000	5000000	834675688858144084964823191	89.431	6	2	2854567650954364	6	0.700

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	0C03CF544771E22B	0.262
1999-08-22T00:00:00	ANONYMOUS	v4_computers	0C03CF544771E22B	0.262
1999-09-14T00:00:00	ANONYMOUS	v4_computers	0C03CF544771E22B	0.262

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-03-31T21:43:57

Oliver Kruse

Threadripper-PC

834675688858144084964823191

8E0895D0951B1F__

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 = 128282700 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 210000, B2 = 5985000 (P-1 stage 2)

B1 = 190000, B2 = 5880973 (P-1 stage 2)

B1 = 210000 (P-1 stage 1)

B1 = 95000, B2 = 1995000 (P-1 stage 2)

B1 = 190000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-20T22:18:07+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