M6 908 203 Mersenne number exponent details

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M6908203

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>>>

is 2 ^6908203 - 1

has 2079577 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	F4F15C52D2C90BDC	double-checked
PRP	001FE9850345552E	PRP-tested

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	138.4345	68.0556%	4000000	414323910	8.3331	7.9700%	146.7676	70.6015%
Target	2⁶⁷	4.3013	65.6716%	45000	900000	0.0290	2.2357%	4.3302	66.4391%
Difference	+5	+134.1333	+2.3839%	+3955000	+413423910	+8.3042	+5.7343%	+142.4374	+4.1624%

Known prime factors (1 factor, 73.1 bits, 0.00105806% 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
6908203	10071112128873032117999	23	73.093	728924159356133 13 × 921643 × 60838187	2021-11-23	921643	60838187	395.16	1.3236	1.9574

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	ANONYMOUS	v4_computers	35000	341250		-		-	-	0.016	-	-	0.798%
2011-11-21	James Heinrich	i7-920	130000	2665000		-		-	-	0.085	-	-	1.985%
2020-01-09	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.581%
2021-11-23	Seth_Tr	Manual testing	4000000	110000000	12		10071112128873032117999	23	73.093	3.091	3.013	6.181	6.530%
2021-11-30	Seth_Tr	Manual testing	4000000	414323910		-	skipped known factor: 10071112128873032117999	-	-	8.333	-	-	7.970%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2001-11-24	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		-	-	2.163	-	-
2018-05-23	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.327	-	-
2020-01-03	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.654	-	-
2020-12-21	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.31	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.62	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.23	-	-

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
2012-08-15	JimBa	Dell	50000	5000000						3	0.995
2017-03-27	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30	mister_phil	v4_computers	F4F15C52D2C90BDC	1.506
2002-01-02	ANONYMOUS	v4_computers	F4F15C52D2C90BDC	1.506

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-11-28

oodaira

com1

10071112128873032117999

001FE9850345552E

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 = 414323910 (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 = 35000, B2 = 341250 (P-1 stage 2)

B1 = 35000 (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: 67.7

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-03-23T17:39:31+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