M6 988 273 Mersenne number exponent details

Residue

Status

L-L

8DA26B549A233F56

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%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

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

+132.5964

+2.3839%

+1955000

+240718650

+4.7312

+4.6766%

+137.3276

+3.8244%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-03	ANONYMOUS	v4_computers	30000	30000		-		-	-	0.009	-	-	0.235%
2011-04-22	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
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-11	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-08-30	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1998-09-20	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1999-11-24	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2002-02-03	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	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.44	-	-

ECM factoring results:

Total ECM effort:	2.984 GHz-days
Estimated T-Level:	1.731

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	2.984

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-09-15	MadPoo	IntLAVH03	50000	5000000						3	0.995
2017-05-12	Yxinity	Elena	50000	5000000						3	0.995
2017-05-13	Yxinity	Manual testing	50000	5000000						3	0.995

date	userid	compid	res64	spent (GHz-days)
2000-01-19	ANONYMOUS	v4_computers	8DA26B549A233F56	1.524
2002-04-28	ANONYMOUS	v4_computers	8DA26B549A233F56	1.524

date

userid

compid

res64

spent (GHz-days)

2000-01-19

ANONYMOUS

v4_computers

8DA26B549A233F56

1.524

2002-04-28

ANONYMOUS

v4_computers

8DA26B549A233F56

1.524

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 = 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=1.73 ~= -11-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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