M3042719 Mersenne number exponent details

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M3042719

<<<

>>>

is 2 ^3042719 - 1

has 915950 decimal digits

takes 0.259 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	35DE12C05029D1D1	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	19.5893	67.6471%	32566261	1856276877	16.2813	13.4718%	35.8706	72.0056%	4.3585%
PrimeNet	2⁶⁰	0.0505	63.3333%	12000	220000	0.0029	2.5217%	0.0534	64.2580%	0.9246%
GPU72	2⁶⁴	1.1698	65.6250%	13000	220000	0.0030	1.4303%	1.1728	66.1167%	0.4917%
Difference	+4	+18.4196	+2.0221%	+32553261	+1856056877	+16.2783	+12.0415%	+34.6978	+5.8889%	+5.8889%

Known prime factors (1 factor, 75.3 bits, 0.00247363% 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
3042719	45420080094517616577359	23	75.266	7463732289198841 73 × 193 × 529756000369	2021-02-15	193	529756000369	3,919.8	3,562.0	6,652.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.147%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-10-07T00:27:00	markr	tiny	110000	2420000		-		-	-	0.029	-	-	2.657%
2016-03-04T23:30:11	Squeeky_Squirrel	P4_2600	195000	5313750	6	-		-	-	0.058	-	-	3.492%
2017-08-20T09:04:29	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.033%
2021-01-12T09:20:52	oodaira	com5	32566261	1856276877	12	-		-	-	16.28	-	-	13.472%
2022-01-26T20:53:27	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.123	-	-	2.532%
2022-02-13T00:12:33	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	7.467%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-12T20:24:00	Sturle Sunde	gilia.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2010-11-01T20:54:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.323	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.645	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.228	-	-
2015-06-03T21:52:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.456	-	-
2017-05-05T02:55:07	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.912	-	-
2022-01-20T22:37:59	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.82	-	-
2018-07-22T23:52:54	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.82	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.636 GHz-days
Estimated T-Level:	2.850

Digits	B1	Curves	Complete	FacMiss
20	11000	57 / 100	0.570	56.391%
25	50000	57 / 280	0.204	81.551%

New Calculation Method

Total ECM effort:	6.636 GHz-days
Estimated T-Level:	2.850

Digits	B1	Complete	FacMiss
20	11000	1.839	15.902%
25	50000	0.166	84.689%
30	250000	0.010	98.982%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	5.006
50000	5000000	45420080094517616577359	14	1.630

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-13T00:02:00	paulie	iMac3.4	50000	5000000						3	0.349
2011-06-08T22:18:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.349
2013-10-03T13:12:00	aubie88	mac_mini	50000	5000000						3	0.349
2016-06-16T22:50:05	Bruce	desk	50000	5000000						3	0.349
2017-08-31T02:32:17	bayanne	iMac	50000	5000000						3	0.349
2020-10-13T00:42:54	mnd9	221Lb	50000	5000000						7	0.815
2020-12-05T00:07:52	mnd9	colab	50000	5000000						7	0.815
2020-12-15T22:56:29	Zenzoma	AM3700X_1	50000	5000000						7	0.815
2021-01-17T09:04:26	RIHATEC	i7-3770K	50000	5000000						7	0.815
2021-02-15T11:15:54	MarkS	desktop-i7	50000	5000000	45420080094517616577359	75.266	14	2	6275992785403133	14	1.630

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	0DC76F43A60CD1__	0.259

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-02-17T04:53:31

Cork

3tits

45420080094517616577359

35DE12C05029D1D1

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 = 32566261, B2 = 1856276877 (P-1 stage 2)

B1 = 32566261 (P-1 stage 1)

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 = 195000, B2 = 5313750 (P-1 stage 2)

B1 = 110000, B2 = 2420000 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

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10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-13T00:12:33+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