M2612719 Mersenne number exponent details

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M2612719

<<<

>>>

is 2 ^2612719 - 1

has 786507 decimal digits

takes 0.181 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	21E061A1774B614D	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	22.8134	67.6471%	2612719	26127190	0.3916	6.2074%	23.2050	69.6553%	2.0083%
PrimeNet	2⁵⁹	0.0294	62.7119%	11000	200000	0.0021	2.6973%	0.0315	63.7176%	1.0058%
GPU72	2⁶³	0.6109	65.0794%	12000	200000	0.0022	1.5318%	0.6131	65.6143%	0.5349%
Difference	+5	+22.2025	+2.5677%	+2600719	+25927190	+0.3894	+4.6756%	+22.5919	+4.0411%	+4.0411%

Known prime factors (1 factor, 74.0 bits, 0.00283167% 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
2612719	18675675861828583070089	23	73.984	3573992431223676 2² × 3² × 7 × 11 × 1289319058883	2020-07-06	11	1289319058883	1,317.9	7,064.9	13,195

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.238%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.781%
2010-11-17T11:34:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.266%
2010-12-14T06:52:00	markr	tiny	100000	2125000		-		-	-	0.021	-	-	2.473%
2014-10-12T23:56:00	Jocelyn Larouche	Manual testing	124566	124566		-		-	-	0.013	-	-	0.942%
2016-05-24T01:15:54	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.039	-	-	3.155%
2017-07-10T01:11:35	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.060	-	-	3.545%
2019-10-14T15:57:29	masser	Manual testing	2612719	26127190	12	-		-	-	0.392	-	-	6.207%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-30T21:50:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-26T15:41:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.118	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.376	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.751	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.430	-	-
2016-01-16T11:43:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.860	-	-
2017-08-28T12:47:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.720	-	-
2019-04-29T13:20:19	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.44	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.239 GHz-days
Estimated T-Level:	1.750

Digits	B1	Curves	Complete	FacMiss
20	11000	35 / 100	0.350	70.345%
25	50000	35 / 280	0.125	88.230%

New Calculation Method

Total ECM effort:	3.239 GHz-days
Estimated T-Level:	1.750

Digits	B1	Complete	FacMiss
20	11000	1.129	32.335%
25	50000	0.102	90.299%
30	250000	0.006	99.374%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	3.054
50000	5000000	18675675861828583070089	2	0.185

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-26T12:23:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.278
2010-06-08T02:00:00	James Hintz	ryan	50000	5000000						3	0.278
2012-11-19T22:50:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.278
2014-08-27T07:21:00	KAMCOBILL	PC20	50000	5000000						3	0.278
2015-11-13T21:19:28	dragon325	Falken-i7-920	50000	5000000						3	0.278
2016-03-29T09:51:01	S36049	Wolle5	50000	5000000						3	0.278
2016-08-19T17:55:18	ANONYMOUS	PD925	50000	5000000						3	0.278
2017-06-11T21:05:01	Bruce	eleven	50000	5000000						3	0.278
2017-10-25T19:36:00	Sebastian Hornbostel	V2	50000	5000000						3	0.278
2018-04-21T05:22:21	deo2016	deo2016.home.new	50000	5000000						3	0.278
2019-02-25T14:31:02	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.278
2020-07-06T04:58:16	GAN	LMS-12	50000	5000000	18675675861828583070089	73.984	2	2	6215303962816393	2	0.185

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	21E061A1774B614D	0.181

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-06T09:52:28

CrypticClue

Manual testing

18675675861828583070089

24CF36173E3E8F87

2020-07-07T08:24:40

marssystems

system11

18675675861828583070089

24CF36173E3E8F87

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 = 2612719, B2 = 26127190 (P-1 stage 2)

B1 = 2612719 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

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

B1 = 200000 (P-1 stage 1)

B1 = 124566 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-07T08:24:40+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