M2534267 Mersenne number exponent details

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M2534267

<<<

>>>

is 2 ^2534267 - 1

has 762891 decimal digits

takes 0.176 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	EB20173E2D0C9B2D	double-checked
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	2⁶⁸	23.5196	67.6471%	3900000	354900000	2.3156	9.6518%	25.8351	70.7697%	3.1226%
PrimeNet	2⁵⁹	0.0303	62.7119%	11000	200000	0.0021	2.6822%	0.0324	63.7120%	1.0001%
GPU72	2⁶³	0.6298	65.0794%	11000	180000	0.0020	1.4355%	0.6318	65.5806%	0.5013%
Difference	+5	+22.8898	+2.5677%	+3889000	+354720000	+2.3135	+8.2163%	+25.2033	+5.1890%	+5.1890%

Known prime factors (1 factor, 80.0 bits, 0.00315550% 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
2534267	1182976720816404259355263	25	79.969	233396228735252493 3 × 199 × 63029 × 6202675861	2020-06-28	63029	6202675861	78,772	33.994	63.480

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.236%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.755%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.264%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.366%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.530%
2011-03-28T18:41:00	James Heinrich	WHS	300000	8000000		-		-	-	0.072	-	-	3.957%
2018-07-29T16:46:53	mikr	MSI	3000000	135000000	12	-		-	-	1.025	-	-	8.260%
2018-08-06T19:34:57	Jocelyn Larouche	low 4M	662000	6620000	12	-		-	-	0.099	-	-	4.177%
2021-09-29T22:53:39	Dylan Delgado	laptop-i78750	3900000	354900000		-		-	-	2.316	-	-	9.652%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-30T23:02:00	Sturle Sunde	papageno.ifi	2⁶⁰	2⁶¹		-	-	0.061	-	-
2012-06-14T15:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.387	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.775	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.474	-	-
2015-11-08T21:03:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.949	-	-
2017-08-08T13:42:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.897	-	-
2019-06-10T09:46:16	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.79	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.869 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	3.869 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.355	25.799%
25	50000	0.122	88.475%
30	250000	0.008	99.249%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.593
50000	5000000	1182976720816404259355263	3	0.276

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-13T09:05:00	Aca Arsov	backo6400	50000	5000000						3	0.276
2010-04-23T23:36:00	James Classen	towerofart	50000	5000000						3	0.276
2012-09-26T23:12:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.276
2014-03-22T12:32:00	Andy Incline	Office-PC	50000	5000000						3	0.276
2015-08-04T10:22:00	guru	w6	50000	5000000						3	0.276
2016-03-04T20:05:59	arnaud	CHAMOT09	50000	5000000						3	0.276
2016-07-07T19:44:42	lettp	Home	50000	5000000						3	0.276
2017-05-04T04:48:26	Ensigma	vps_sing	50000	5000000						3	0.276
2017-09-27T20:47:17	Lelikoid	QH	50000	5000000						3	0.276
2018-02-05T04:14:54	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2018-10-27T09:52:14	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2020-05-27T16:56:24	Brett Walker	brain	50000	5000000						3	0.276
2020-06-15T08:28:21	Summy	CHB	50000	5000000						3	0.276
2020-06-28T23:45:12	GAN	GAN-HP	50000	5000000	1182976720816404259355263	79.969	3	2	5451866940877979	3	0.276

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	EB20173E2D0C9B2D	0.176
2018-06-08T12:06:05	kkmrkkblmbrbk	old	EB20173E2D0C9B2D	0.176

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-06-29T03:31:53

CrypticClue

Manual testing

1182976720816404259355263

E342299E1F92A1A3

2020-09-25T03:22:10

arnaud

stm-11-010

1182976720816404259355263

E342299E1F92A1A3

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 = 3900000, B2 = 354900000 (P-1 stage 2)

B1 = 3000000, B2 = 135000000 (P-1 stage 2)

B1 = 3900000 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 662000, B2 = 6620000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 662000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-09-29T22:53:39+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