M2065117 Mersenne number exponent details

Residue

Status

L-L

52FE41AC7300FB17

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	14.3885	68.6567%	500000	15000000	0.1230	5.1428%	14.5115	70.2686%	1.6119%
PrimeNet	2⁵⁸	0.0186	63.7931%	9000	160000	0.0016	2.6693%	0.0202	64.7596%	0.9665%
GPU72	2⁶²	0.2975	66.1290%	9000	130000	0.0015	1.3657%	0.2990	66.5916%	0.4626%
Difference	+5	+14.0910	+2.5277%	+491000	+14870000	+0.1215	+3.7771%	+14.2125	+3.6770%	+3.6770%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.3885

68.6567%

500000

15000000

0.1230

5.1428%

14.5115

70.2686%

1.6119%

PrimeNet

2⁵⁸

0.0186

63.7931%

9000

160000

0.0016

2.6693%

0.0202

64.7596%

0.9665%

GPU72

2⁶²

0.2975

66.1290%

9000

130000

0.0015

1.3657%

0.2990

66.5916%

0.4626%

Difference

+14.0910

+2.5277%

+491000

+14870000

+0.1215

+3.7771%

+14.2125

+3.6770%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2065117	12786033331027809841	20	63.471	3095716448760 2³ × 3 × 5 × 13 × 229 × 8665649	2009-10-28	229	8665649	1.1556	0.0450	0.0841
2065117	202991992605844799719	21	67.460	49147818890127 3 × 677 × 24198827617	2022-08-18	677	24198827617	26.316	125.69	234.76

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2065117

12786033331027809841

63.471

3095716448760
2³ × 3 × 5 × 13 × 229 × 8665649

2009-10-28

229

8665649

1.1556

0.0450

0.0841

2065117

202991992605844799719

67.460

49147818890127
3 × 677 × 24198827617

2022-08-18

677

24198827617

26.316

125.69

234.76

exponent	prime factors	composite factor	digits	bits*
2065117	12786033331027809841 202991992605844799719	2595462383390082329658795153539862234679	40	130.931

exponent

prime factors

composite factor

digits

bits*

2065117

12786033331027809841
202991992605844799719

2595462383390082329658795153539862234679

130.931

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.275%
2009-07-23T23:41:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.017%
2016-03-16T13:43:09	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 12786033331027809841	-	-	0.123	-	-	5.143%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T08:13:23	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.074	-	-
2009-01-03T04:51:00	Sturle Sunde	graun.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
TF assumed completed to 67 but no detailed record exists
2022-08-18T09:36:57	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	202991992605844799719	67.460	21	11.93	0.276	24.22

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.961 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:	2.961 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.282	27.747%
25	50000	0.118	88.855%
30	250000	0.008	99.252%

ECM Summary

B1	B2	factor	curves	GHz-days
		12786033331027809841	1	0.00000e+0
50000	5000000		3	0.255
50000	6542544		7	0.669
50000	6750000		21	2.037

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-10T07:32:00	alan145	Bear4	50000	5000000						3	0.255
2009-10-28T15:17:00	KAMCOBILL	PC01			12786033331027809841	63.471		1		1	-
2021-08-12T09:32:18	Dylan Delgado	colab	50000	6750000						7	0.679
2021-11-17T06:00:31	Dylan Delgado	colab	50000	6750000						7	0.679
2022-04-22T06:11:47	Dylan Delgado	colab	50000	6750000						7	0.679
2022-07-04T03:36:29	debrouxl	dl380g9-1	50000	6542544						7	0.669

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	52FE41AC7300FB17	0.136

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

52FE41AC7300FB17

0.136

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T12:14:14

Oliver Kruse

GTX-3

12786033331027809841

694F656927F4F9__

2017-11-15T23:12:32

ATH

ec2-1xf

12786033331027809841

694F656927F4F9__

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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