M4112579 Mersenne number exponent details

Residue

Status

L-L

C44C45D4B2D78F7F

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	7.2251	67.1642%	125000	2343750	0.0445	3.1640%	7.2696	68.2031%	1.0389%
PrimeNet	2⁶¹	0.0747	63.9344%	17000	340000	0.0063	2.8242%	0.0809	64.9530%	1.0186%
GPU72	2⁶⁵	1.7740	66.1538%	22000	400000	0.0077	1.8096%	1.7817	66.7663%	0.6125%
Difference	+2	+5.4511	+1.0103%	+103000	+1943750	+0.0368	+1.3544%	+5.4879	+1.4368%	+1.4368%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.2251

67.1642%

125000

2343750

0.0445

3.1640%

7.2696

68.2031%

1.0389%

PrimeNet

2⁶¹

0.0747

63.9344%

17000

340000

0.0063

2.8242%

0.0809

64.9530%

1.0186%

GPU72

2⁶⁵

1.7740

66.1538%

22000

400000

0.0077

1.8096%

1.7817

66.7663%

0.6125%

Difference

+5.4511

+1.0103%

+103000

+1943750

+0.0368

+1.3544%

+5.4879

+1.4368%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4112579	95685642674772479359	20	66.375	11633289314901 3 × 3877763104967	2016-04-12	3	3877763104967	4.4571	38,208	71,362

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4112579

95685642674772479359

66.375

11633289314901
3 × 3877763104967

2016-04-12

3877763104967

4.4571

38,208

71,362

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-24T22:42:00	Carsten Kossendey	durandal	20000	300000		-		-	-	0.006	-	-	1.215%
2011-08-02T04:04:00	harlee	P4_2600	40000	580000		-		-	-	0.013	-	-	1.775%
2013-06-20T00:54:00	Squeeky_Squirrel	T7500_2200	125000	2343750		-		-	-	0.044	-	-	3.164%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.075	-	-
2010-11-27T04:22:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.075	-	-
2011-07-01T19:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.388	-	-
2016-02-23T16:29:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.239	-	-
2013-09-07T07:51:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.477	-	-
2013-11-01T12:14:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.909	-	-
2015-05-31T21:23:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.817	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.629 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.629 GHz-days
Estimated T-Level:	0.450

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		6	1.086
50000	5000000	95685642674772479359	3	0.543

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-11-16T09:20:00	S00030	vd01	50000	5000000						3	0.543
2012-11-29T22:06:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.543
2016-04-12T01:27:05	Sid & Andy	Mrs_Potato_Head	50000	5000000	95685642674772479359	66.375	3	2		3	0.543

date	userid	compid	res64	spent (GHz-days)
1999-10-15T00:00:00	ANONYMOUS	v4_computers	C44C45D4B2D78F7F	0.513

date

userid

compid

res64

spent (GHz-days)

1999-10-15T00:00:00

ANONYMOUS

v4_computers

C44C45D4B2D78F7F

0.513

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-14T21:24:42

Oliver Kruse

GTX-3

95685642674772479359

3A5EA4B55E155A__

2017-12-24T01:10:33

kkmrkkblmbrbk

c4.xlarge

95685642674772479359

3A5EA4B55E155A__

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 = 125000, B2 = 2343750 (P-1 stage 2)

B1 = 125000 (P-1 stage 1)

B1 = 40000, B2 = 580000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

B1 = 20000, B2 = 300000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

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