M6 904 883 Mersenne number exponent details

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M6904883

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is 2 ^6904883 - 1

has 2078577 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	26CBC66F7A9849AA	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	138.5011	68.0556%	1000000	30000000	0.8157	4.5580%	139.3168	69.5116%
Target	2⁶⁷	4.3033	65.6716%	45000	900000	0.0290	2.2355%	4.3323	66.4390%
Difference	+5	+134.1977	+2.3839%	+955000	+29100000	+0.7868	+2.3225%	+134.9845	+3.0725%

Known prime factors:
No known factors for M6904883

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-24	ANONYMOUS	v4_computers	35000	446250		-		-	-	0.018	-	-	0.868%
2002-03-31	ANONYMOUS	v4_computers	30000	270000		-		-	-	0.014	-	-	0.704%
2012-08-10	Nesowa	EPC	85000	1487500		-		-	-	0.051	-	-	1.558%
2019-04-26	takahashi	vaio	300000	5000000	6	-		-	-	0.176	-	-	2.681%
2021-05-11	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
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1998-11-28	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-06-19	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	-	-
2016-03-31	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.164	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.329	-	-
2019-11-30	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.658	-	-
2020-12-20	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.32	-	-
2021-08-16	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.63	-	-
2021-10-10	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.26	-	-

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
2012-08-13	Clown_Royal	lab2	50000	5000000						3	0.995
2017-03-24	mensasnem	thomas	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-21	ANONYMOUS	v4_computers	26CBC66F7A9849AA	1.506
2003-01-09	ANONYMOUS	v4_computers	26CBC66F7A9849AA	1.506

PRP results:
No PRP results for M6904883

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 = 1487500 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 446250 (P-1 stage 2)

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

B1 = 35000 (P-1 stage 1)

B1 = 30000 (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