M6 909 781 Mersenne number exponent details

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M6909781

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is 2 ^6909781 - 1

has 2080052 decimal digits

takes 1.507 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	B2E3703E7B092C6E	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	138.4029	68.0556%	1000000	30000000	0.8157	4.5584%	139.2186	69.5117%
Target	2⁶⁷	4.3003	65.6716%	45000	900000	0.0290	2.2357%	4.3292	66.4391%
Difference	+5	+134.1026	+2.3839%	+955000	+29100000	+0.7868	+2.3226%	+134.8894	+3.0726%

Known prime factors:
No known factors for M6909781

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-06-10	Roman Maznichenko	WorkShop	85000	1572500		-		-	-	0.052	-	-	1.581%
2019-05-09	takahashi	vaio	300000	5000000	6	-		-	-	0.176	-	-	2.681%
2021-05-15	takahashi	vaio	1000000	30000000	12	-		-	-	0.816	-	-	4.558%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-29	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2004-06-12	Sturle Sunde	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2004-08-04	Sturle Sunde	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	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.081	-	-
2016-04-01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.163	-	-
2018-02-25	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.326	-	-
2019-12-13	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.652	-	-
2020-12-23	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.30	-	-
2021-08-13	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.61	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.21	-	-

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
2012-08-11	JimBa	Dell	50000	5000000						3	0.995
2017-03-28	h0b0byter99	camserve	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06	ANONYMOUS	v4_computers	B2E3703E7B092C6E	1.507
2001-09-10	ANONYMOUS	v4_computers	B2E3703E7B092C6E	1.507

PRP results:
No PRP results for M6909781

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 300000, B2 = 5000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 85000, B2 = 1572500 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

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