M2079719 Mersenne number exponent details

Residue

Status

L-L

AA62A93BD4C799EF

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	14.2875	68.6567%	500000	15000000	0.1230	5.1472%	14.4105	70.2700%	1.6133%
PrimeNet	2⁵⁸	0.0185	63.7931%	9000	160000	0.0016	2.6729%	0.0201	64.7609%	0.9678%
GPU72	2⁶²	0.2954	66.1290%	9000	130000	0.0015	1.3677%	0.2969	66.5923%	0.4633%
Difference	+5	+13.9921	+2.5277%	+491000	+14870000	+0.1215	+3.7795%	+14.1136	+3.6777%	+3.6777%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.2875

68.6567%

500000

15000000

0.1230

5.1472%

14.4105

70.2700%

1.6133%

PrimeNet

2⁵⁸

0.0185

63.7931%

9000

160000

0.0016

2.6729%

0.0201

64.7609%

0.9678%

GPU72

2⁶²

0.2954

66.1290%

9000

130000

0.0015

1.3677%

0.2969

66.5923%

0.4633%

Difference

+13.9921

+2.5277%

+491000

+14870000

+0.1215

+3.7795%

+14.1136

+3.6777%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2079719	4627188474058981223	19	62.005	1112455210069 7 × 158922172867	2009-11-02	7	158922172867	0.3004	825.48	1,541.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2079719

4627188474058981223

62.005

1112455210069
7 × 158922172867

2009-11-02

158922172867

0.3004

825.48

1,541.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.276%
2009-07-25T16:47:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.018%
2016-03-16T13:44:52	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.147%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	Peter Yu	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T08:46:53	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.074	-	-
2009-01-03T06:23:00	Sturle Sunde	interavia.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.138 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	3.138 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.268	28.148%
25	50000	0.117	88.999%
30	250000	0.007	99.270%

ECM Summary

B1	B2	factor	curves	GHz-days
		4627188474058981223	1	0.00000e+0
50000	50000		7	0.355
50000	5000000		17	1.445
50000	6318825		7	0.659
50000	6744577		7	0.679

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-06T10:11:00	Battlemaxx	Maxx_mom	50000	5000000						3	0.255
2009-11-02T11:00:00	KAMCOBILL	PC01			4627188474058981223	62.005		1		1	-
2021-09-08T08:39:30	JackBlock	school1	50000	50000						7	0.355
2021-09-20T04:46:54	Ahmed Azhad	c5.azf2	50000	6744577						7	0.679
2022-01-24T02:07:49	MarkS	desktop-i7	50000	5000000						7	0.595
2022-05-24T14:10:10	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.595
2022-07-13T17:30:27	debrouxl	dl380g9-1	50000	6318825						7	0.659

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	Peter Yu	v4_computers	AA62A93BD4C799EF	0.137

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

Peter Yu

v4_computers

AA62A93BD4C799EF

0.137

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T16:16:15

Oliver Kruse

GTX-0

4627188474058981223

F629EF301A9134__

2017-11-16T13:14:02

kkmrkkblmbrbk

c4.xlarge

4627188474058981223

F629EF301A9134__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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