M6606191 Mersenne number exponent details

Residue

Status

L-L

B24C4A78D715C787

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	4.4979	65.6716%	80000	1340000	0.0404	2.7537%	4.5383	66.6170%	0.9453%
PrimeNet	2⁶³	0.2416	63.4921%	28000	700000	0.0176	3.1362%	0.2592	64.6370%	1.1449%
GPU72	2⁶⁷	4.4979	65.6716%	40000	800000	0.0221	2.0958%	4.5200	66.3911%	0.7195%
Difference	-	-	-	+40000	+540000	+0.0183	+0.6579%	+0.0183	+0.2259%	+0.2259%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.4979

65.6716%

80000

1340000

0.0404

2.7537%

4.5383

66.6170%

0.9453%

PrimeNet

2⁶³

0.2416

63.4921%

28000

700000

0.0176

3.1362%

0.2592

64.6370%

1.1449%

GPU72

2⁶⁷

4.4979

65.6716%

40000

800000

0.0221

2.0958%

4.5200

66.3911%

0.7195%

Difference

+40000

+540000

+0.0183

+0.6579%

+0.0183

+0.2259%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6606191	47973309178836922926289	23	75.345	3630935676764184 2³ × 3 × 101 × 1497910757741	2017-01-02	101	1497910757741	1,645.7	22,180	41,425

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6606191

47973309178836922926289

75.345

3630935676764184
2³ × 3 × 101 × 1497910757741

2017-01-02

101

1497910757741

1,645.7

22,180

41,425

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-06-23T00:00:00	barryh	v4_computers	30000	307500		-		-	-	0.012	-	-	1.500%
2012-07-03T18:57:00	Nesowa	Laptop	80000	1340000		-		-	-	0.040	-	-	2.754%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.046	-	-
1998-07-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.093	-	-
1999-12-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.242	-	-
2014-06-29T01:13:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.297	-	-
2014-07-07T20:17:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.566	-	-
2015-11-04T20:31:47	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.131	-	-
2016-03-29T12:12:59	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.262	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.710 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.710 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.855
50000	5000000	47973309178836922926289	3	0.855

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-06-16T00:46:00	Michael W.	penryn	50000	5000000						3	0.855
2017-01-03T01:48:29	Bruce	Desk2	50000	5000000	47973309178836922926289	75.345	3	2		3	0.855

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	schaz	v4_computers	3D8FA2D68D5971__	1.238
2000-07-25T00:00:00	ANONYMOUS	v4_computers	B24C4A78D715C787	1.238
2001-07-29T00:00:00	barryh	v4_computers	B24C4A78D715C787	1.238

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-27T19:25:05

pew

desktop

47973309178836922926289

AC9B8A3C73428A__

2018-11-05T08:28:51

Oliver Kruse

GTX-2

47973309178836922926289

AC9B8A3C73428A__

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 = 80000, B2 = 1340000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 30000, B2 = 307500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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