M6 906 209 Mersenne number exponent details

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M6906209

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is 2 ^6906209 - 1

has 2078977 decimal digits

takes 1.506 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	E0FF34EE2F17D34D	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	138.4745	68.0556%	4000000	421309350	8.4535	7.9881%	146.9279	70.6073%
Target	2⁶⁷	4.3025	65.6716%	45000	900000	0.0290	2.2355%	4.3314	66.4391%
Difference	+5	+134.1720	+2.3839%	+3955000	+420409350	+8.4245	+5.7525%	+142.5965	+4.1682%

Known prime factors:
No known factors for M6906209

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-24	Phantomas	v4_computers	30000	270000		-		-	-	0.014	-	-	0.704%
2011-11-20	James Heinrich	i7-920	130000	2665000		-		-	-	0.085	-	-	1.985%
2020-01-08	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.581%
2021-11-21	Seth_Tr	Manual testing	4000000	110000000	12	-		-	-	3.091	-	-	6.529%
2021-11-29	Seth_Tr	Manual testing	4000000	421309350		-		-	-	8.453	-	-	7.988%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	mhoney	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-29	Will Edgington	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1998-08-02	Will Edgington	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1998-09-13	Will Edgington	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1999-01-29	Will Edgington	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-07-01	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.284	-	-
2014-02-18	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.541	-	-
2015-06-21	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.082	-	-
2016-04-01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.164	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.328	-	-
2019-12-02	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.656	-	-
2020-12-20	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.31	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.63	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.25	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-08-12	Christopher Tompkins	iMac2	50000	5000000						3	0.995
2017-03-26	h0b0byter99	camserve	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06	ANONYMOUS	v4_computers	E0FF34EE2F17D34D	1.506
2001-09-10	Phantomas	v4_computers	E0FF34EE2F17D34D	1.506

PRP results:
No PRP results for M6906209

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 = 4000000, B2 = 421309350 (P-1 stage 2)

B1 = 4000000, B2 = 110000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 600000, B2 = 12000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 130000, B2 = 2665000 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 30000, B2 = 270000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.8

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-04-26T21:34:10+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