M7079707 Mersenne number exponent details

Residue

Status

L-L

A779186AC8BE0C4C

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	2⁷³	270.1869	68.4932%	5000000	125000000	3.6481	6.2685%	273.8350	70.4682%	1.9750%
PrimeNet	2⁶³	0.2254	63.4921%	30000	800000	0.0227	3.3196%	0.2482	64.7040%	1.2119%
GPU72	2⁶⁷	4.1971	65.6716%	45000	1000000	0.0307	2.3041%	4.2277	66.4626%	0.7910%
Difference	+6	+265.9899	+2.8215%	+4955000	+124000000	+3.6174	+3.9644%	+269.6073	+4.0056%	+4.0056%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

270.1869

68.4932%

5000000

125000000

3.6481

6.2685%

273.8350

70.4682%

1.9750%

PrimeNet

2⁶³

0.2254

63.4921%

30000

800000

0.0227

3.3196%

0.2482

64.7040%

1.2119%

GPU72

2⁶⁷

4.1971

65.6716%

45000

1000000

0.0307

2.3041%

4.2277

66.4626%

0.7910%

Difference

+265.9899

+2.8215%

+4955000

+124000000

+3.6174

+3.9644%

+269.6073

+4.0056%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7079707	928319223277628296640447231087	30	99.551	65561980409473746345749 7 × 23 × 59² × 19181 × 732209 × 8329441	2016-03-20	732209	8329441	2.702e+10	0.3624	0.4712

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

7079707

928319223277628296640447231087

99.551

65561980409473746345749
7 × 23 × 59² × 19181 × 732209 × 8329441

2016-03-20

732209

8329441

2.702e+10

0.3624

0.4712

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08T00:00:00	ANONYMOUS	v4_computers	25000	93750		-		-	-	0.009	-	-	0.381%
2002-08-10T00:00:00	ANONYMOUS	v4_computers	35000	533750		-		-	-	0.020	-	-	0.797%
2011-12-30T16:35:00	bcp19	Manual testing	85000	1551250		-		-	-	0.052	-	-	1.393%
2014-08-17T13:42:00	Nesowa	newfs	250000	3812500		-		-	-	0.140	-	-	2.193%
2016-03-20T13:05:30	mikr	S052	5000000	125000000	12		928319223277628296640447231087	30	99.551	3.648	3.088	7.296	6.269%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.087	-	-
1998-06-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.087	-	-
2005-07-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.225	-	-
2012-02-19T13:10:00	Never Odd Or Even	Manual testing	2⁶³	2⁶⁴		-	-	0.277	-	-
2012-02-19T13:10:00	Never Odd Or Even	Manual testing	2⁶⁴	2⁶⁵		-	-	0.528	-	-
2012-02-19T13:10:00	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	1.056	-	-
2012-03-14T12:20:00	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	2.111	-	-
2012-03-14T12:20:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	4.222	-	-
2013-03-10T21:02:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	8.444	-	-
2013-03-10T21:02:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	16.89	-	-
2013-03-13T01:14:00	Never Odd Or Even	Manual testing	2⁷⁰	2⁷¹		-	-	33.78	-	-
2013-07-02T17:39:00	Never Odd Or Even	Manual testing	2⁷¹	2⁷²		-	-	67.55	-	-
2013-07-02T17:39:00	Never Odd Or Even	Manual testing	2⁷²	2⁷³		-	-	135.1	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.995 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.995 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.995

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-10-12T00:09:00	ANONYMOUS	i5-nb	50000	5000000						3	0.995

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	Joel Armengaud	v4_computers	A779186AC8BE0C4C	1.544
2002-08-10T00:00:00	ANONYMOUS	v4_computers	A779186AC8BE0C4C	1.544

date

userid

compid

res64

spent (GHz-days)

1999-04-02T00:00:00

Joel Armengaud

v4_computers

A779186AC8BE0C4C

1.544

2002-08-10T00:00:00

ANONYMOUS

v4_computers

A779186AC8BE0C4C

1.544

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-02-05T13:53:54

-p95holder- @bopoh13

t_i3-2100

928319223277628296640447231087

B7383E9E40D671__

2019-03-11T15:03:04

kkmrkkblmbrbk

c5.large

928319223277628296640447231087

B7383E9E40D67196

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 = 5000000, B2 = 125000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 250000, B2 = 3812500 (P-1 stage 2)

B1 = 250000 (P-1 stage 1)

B1 = 85000, B2 = 1551250 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 533750 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

B1 = 25000, B2 = 93750 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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