M6 988 271 Mersenne number exponent details

≡

M6988271

<<<

>>>

is 2 ^6988271 - 1

has 2103680 decimal digits

takes 1.524 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	5E7A1727D9F43A7C	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	136.8484	68.0556%	2000000	241618650	4.7601	6.9165%	141.6085	70.2650%
Target	2⁶⁷	4.2520	65.6716%	45000	900000	0.0290	2.2399%	4.2809	66.4406%
Difference	+5	+132.5964	+2.3839%	+1955000	+240718650	+4.7312	+4.6766%	+137.3276	+3.8244%

Known prime factors:
No known factors for M6988271

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-22	ANONYMOUS	v4_computers	25000	87500		-		-	-	0.009	-	-	0.432%
2011-06-09	Carsten Kossendey	leela	445000	13572500		-		-	-	0.367	-	-	3.528%
2021-11-07	Seth_Tr	Manual testing	2000000	58000000	12	-		-	-	1.597	-	-	5.524%
2021-12-06	Seth_Tr	Manual testing	2000000	241618650		-		-	-	4.760	-	-	6.917%

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		-	-	0.088	-	-
1999-12-01	JC	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2002-01-22	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-14	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.535	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.069	-	-
2016-04-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.139	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.277	-	-
2020-04-10	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.555	-	-
2021-08-13	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.11	-	-
2021-09-06	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.22	-	-
2021-09-26	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.44	-	-

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
2012-09-12	ATH	quad	50000	5000000						3	0.995
2017-05-18	BloodIce	URM2	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	89085656F5090B__	1.524
2000-01-19	JC	v4_computers	5E7A1727D9F43A7C	1.524
2002-11-02	oerwin	v4_computers	5E7A1727D9F43A7C	1.524

PRP results:
No PRP results for M6988271

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 = 2000000, B2 = 241618650 (P-1 stage 2)

B1 = 2000000, B2 = 58000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 445000, B2 = 13572500 (P-1 stage 2)

B1 = 445000 (P-1 stage 1)

B1 = 25000, B2 = 87500 (P-1 stage 2)

B1 = 25000 (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

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