M3026951 Mersenne number exponent details

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M3026951

<<<

>>>

is 2 ^3026951 - 1

has 911204 decimal digits

takes 0.258 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	E81036C2EF7C3232	double-checked
PRP	F74CE07D85FCD85C	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	39.4413	68.1159%	32656058	1861395306	16.3262	12.6553%	55.7674	72.1509%	4.0350%
PrimeNet	2⁶⁰	0.0507	63.3333%	12000	220000	0.0029	2.5193%	0.0536	64.2571%	0.9237%
GPU72	2⁶⁴	1.1759	65.6250%	13000	220000	0.0030	1.4288%	1.1789	66.1162%	0.4912%
Difference	+5	+38.2654	+2.4909%	+32643058	+1861175306	+16.3232	+11.2264%	+54.5886	+6.0348%	+6.0348%

Known prime factors (1 factor, 82.0 bits, 0.00270807% 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
3026951	4743084652918815620891183	25	81.972	783475624963670641 29 × 79 × 341979757731851	2021-04-10	79	341979757731851	180,737	2,299,396	4,294,631

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	-	-	0.121%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.200%
2010-10-13T06:34:00	markr	tiny	115000	2357500		-		-	-	0.029	-	-	2.367%
2016-04-26T20:25:53	harlee	P4_2600	205000	5637500	12	-		-	-	0.062	-	-	3.197%
2017-06-07T01:13:26	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.400%
2020-01-29T07:20:05	oodaira	com5	32656058	1861395306	12	-		-	-	16.33	-	-	12.655%
2022-01-26T04:01:33	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.841%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-01-29T21:34:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-10-06T19:25:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.324	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.649	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.234	-	-
2015-06-02T19:30:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.469	-	-
2017-05-01T03:38:02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.937	-	-
2022-01-20T22:37:58	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.87	-	-
2018-07-16T08:59:48	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.87	-	-
2021-03-25T10:40:28	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.444 GHz-days
Estimated T-Level:	3.200

Digits	B1	Curves	Complete	FacMiss
20	11000	64 / 100	0.640	52.560%
25	50000	64 / 280	0.229	79.534%

New Calculation Method

Total ECM effort:	7.444 GHz-days
Estimated T-Level:	3.200

Digits	B1	Complete	FacMiss
20	11000	2.462	8.530%
25	50000	0.228	79.632%
30	250000	0.014	98.574%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	6.630
50000	5000000	4743084652918815620891183	7	0.814

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-07T01:34:00	James Hintz	4115	50000	5000000						3	0.349
2011-06-02T04:39:00	Smurgs	Praca	50000	5000000						3	0.349
2013-09-21T12:00:00	Bruce	Ocelot-1	50000	5000000						3	0.349
2016-01-23T13:02:21	Bruce	Desk7	50000	5000000						3	0.349
2017-08-21T07:44:47	jafarism	jafarism-r07	50000	5000000						3	0.349
2020-10-02T07:30:47	mnd9	libproj	50000	5000000						7	0.814
2020-10-27T10:43:43	lycorn	colab_A	50000	5000000						7	0.814
2020-12-02T12:08:04	GAN	KA-HP	50000	5000000						7	0.814
2021-01-04T05:36:08	Zenzoma	AMD3970X	50000	5000000						7	0.814
2021-02-03T20:16:57	Zenzoma	AMD3970X	50000	5000000						7	0.814
2021-03-05T03:12:50	RIHATEC	i7-3770K	50000	5000000						7	0.814
2021-04-10T05:38:25	Zenzoma	AMD3970X	50000	5000000	4743084652918815620891183	81.972	7	2	2904880523917887	7	0.814

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	mijutu	v4_computers	E81036C2EF7C3232	0.258
1999-11-04T00:00:00	ANONYMOUS	v4_computers	E81036C2EF7C3232	0.258
2000-05-31T00:00:00	ANONYMOUS	v4_computers	E81036C2EF7C3232	0.258
2001-02-11T00:00:00	ANONYMOUS	v4_computers	E81036C2EF7C3232	0.258

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-12T06:06:38

Joe S.

VMWare3

4743084652918815620891183

F74CE07D85FCD85C

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 = 32656058, B2 = 1861395306 (P-1 stage 2)

B1 = 32656058 (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 = 205000, B2 = 5637500 (P-1 stage 2)

B1 = 115000, B2 = 2357500 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

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10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-26T04:01:33+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