M6 976 223 Mersenne number exponent details

Residue

Status

L-L

8DF2365F9B9B4C8C

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	137.0847	68.0556%	4000000	110000000	3.0907	6.5360%	140.1754	70.1435%
Target	2⁶⁷	4.2593	65.6716%	45000	900000	0.0290	2.2393%	4.2883	66.4403%
Difference	+5	+132.8254	+2.3839%	+3955000	+109100000	+3.0618	+4.2967%	+135.8872	+3.7031%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

137.0847

68.0556%

4000000

110000000

3.0907

6.5360%

140.1754

70.1435%

Target

2⁶⁷

4.2593

65.6716%

45000

900000

0.0290

2.2393%

4.2883

66.4403%

Difference

+132.8254

+2.3839%

+3955000

+109100000

+3.0618

+4.2967%

+135.8872

+3.7031%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-16	ANONYMOUS	v4_computers	35000	341250		-		-	-	0.016	-	-	0.800%
2011-12-01	James Heinrich	Q6600	135000	2835000		-		-	-	0.089	-	-	2.034%
2020-01-29	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.585%
2021-11-22	Seth_Tr	Manual testing	4000000	110000000	12	-		-	-	3.091	-	-	6.536%

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	2⁶²		-	-	0.088	-	-
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1998-07-29	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1998-08-16	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1998-10-04	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2004-10-18	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.536	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.071	-	-
2016-04-26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.142	-	-
2018-02-26	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.285	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.569	-	-
2021-08-08	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.14	-	-
2021-09-15	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.28	-	-
2021-09-19	Jon Pace	Manual testing	2⁷¹	2⁷²		-	-	68.56	-	-

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
2012-09-13	Clown_Royal	lab	50000	5000000						3	0.995
2017-05-07	arnaud	CHAMOT06	50000	5000000						3	0.995

date	userid	compid	res64	spent (GHz-days)
1999-04-23	Orion	v4_computers	8DF2365F9B9B4C8C	1.521
2001-12-22	ANONYMOUS	v4_computers	8DF2365F9B9B4C8C	1.521

date

userid

compid

res64

spent (GHz-days)

1999-04-23

Orion

v4_computers

8DF2365F9B9B4C8C

1.521

2001-12-22

ANONYMOUS

v4_computers

8DF2365F9B9B4C8C

1.521

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 = 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 = 135000, B2 = 2835000 (P-1 stage 2)

B1 = 135000 (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

this exponent TF target: 67

TF double-checked to: 67.8

ECM T-Level=1.15 ~= -13-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