M3083023 Mersenne number exponent details

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M3083023

<<<

>>>

is 2 ^3083023 - 1

has 928083 decimal digits

takes 0.262 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	2⁷⁰	77.5053	68.5714%	9000000	23050959750	156.0397	14.2082%	233.5450	73.0369%	4.4654%
Target	2⁶⁴	1.1545	65.6250%	14000	220000	0.0031	1.4680%	1.1576	66.1296%	0.5046%
Difference	+6	+76.3508	+2.9464%	+8986000	+23050739750	+156.0366	+12.7402%	+232.3874	+6.9072%	+3.9608%

Known prime factors (1 factor, 127.0 bits, 0.00411950% 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
3083023	170749644674983140373659749189793240527	39	127.005	27691918723114154577124424499881 1163 × 1511 × 25819 × 35279 × 1376567 × 12567700751	2023-01-05	1376567	12567700751	5.994e+10	84.663	157.83

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	-	-	0.162%
2008-10-29T00:21:00	Jayson King	atlas	40000	640000		-		-	-	0.009	-	-	1.150%
2011-08-18T15:06:00	harlee	P4_2600	100000	2125000		-		-	-	0.026	-	-	1.994%
2016-04-14T05:13:12	Jocelyn Larouche	Manual testing	200000	6188987	6	-		-	-	0.065	-	-	2.918%
2018-03-19T18:15:00	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	6.826%
2023-01-05T21:38:06	Sid & Andy	Hockey_Puck	9000000	23050959750			170749644674983140373659749189793240527	39	127.005	156.0	0.525	312.1	14.208%

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	-	-
2009-02-12T23:55:00	Sturle Sunde	eberlin.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-11-12T21:56:00	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		-	-	2.424	-	-
2017-05-18T12:32:20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.848	-	-
2018-08-10T10:59:50	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.70	-	-
2021-03-10T09:10:08	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.39	-	-
2022-05-31T08:52:46	mikr	Manual testing	2⁶⁹	2⁷⁰		-	-	38.78	-	-

ECM factoring results:

Total ECM effort:	91.724 GHz-days
Estimated T-Level:	25.882

Digits	B1	Complete	FacMiss
20	11000	30.215	0.000%
25	50000	2.796	6.108%
30	250000	0.176	83.832%
35	1000000	0.008	99.179%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		778	90.78
50000	6750000		7	0.943

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-07T15:16:00	S530729	AMD-X5200	50000	5000000						3	0.350
2011-07-19T10:24:00	Smurgs	Praca	50000	5000000						3	0.350
2013-11-07T15:39:00	Bruce	fx6840-21	50000	5000000						3	0.350
2016-05-01T19:47:34	ANONYMOUS		50000	5000000						3	0.350
2017-10-11T14:38:08	driveByUpgrades	AMD8	50000	5000000						3	0.350
2020-10-22T14:49:38	mnd9	kitchen	50000	5000000						7	0.817
2020-11-19T00:36:50	mnd9	27016b	50000	5000000						7	0.817
2020-12-27T03:26:04	lycorn	colab_test	50000	6750000						7	0.943
2021-01-29T18:28:52	Zenzoma	AMD3970X	50000	5000000						7	0.817
2021-02-27T22:09:30	mnd9	kitchen	50000	5000000						7	0.817
2021-04-03T16:02:27	Zenzoma	AMD3970X	50000	5000000						7	0.817
2021-05-27T20:09:22	GAN	KL-SCH09	50000	5000000						7	0.817
2021-07-05T07:31:38	Yizhe Huang	clb3	50000	5000000						7	0.817
2021-08-20T06:54:46	daveward2005	d12436	50000	5000000						7	0.817
2021-10-31T13:57:31	daveward2005	Dave2	50000	5000000						7	0.817
2021-02-15T17:21:28	kerni3	Manual testing	50000	5000000						350	40.84
2021-02-15T17:21:28	kerni3	Manual testing	50000	5000000						350	40.84

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	705713D90FBB77__	0.262
1999-09-22T00:00:00	ANONYMOUS	v4_computers	B1DFECCDBD40DD__	0.262

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-01-07T11:34:09

LordJulius

WhiteBox

170749644674983140373659749189793240527

13967931F8BE0613

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 = 9000000, B2 = 23050959750 (P-1 stage 2)

B1 = 9000000 (P-1 stage 1)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 200000, B2 = 6188987 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 40000, B2 = 640000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2023-01-07T11:34:09+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