M2195467 Mersenne number exponent details

Residue

Status

L-L

3E605A5D4213A2D6

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	13.5342	67.1642%	500000	15000000	0.1230	5.1808%	13.6572	68.8653%	1.7012%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8620%	0.0193	63.1546%	1.0856%
GPU72	2⁶²	0.2798	64.5161%	11000	160000	0.0018	1.5710%	0.2817	65.0736%	0.5574%
Difference	+5	+13.2544	+2.6481%	+489000	+14840000	+0.1212	+3.6098%	+13.3755	+3.7918%	+3.7918%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.5342

67.1642%

500000

15000000

0.1230

5.1808%

13.6572

68.8653%

1.7012%

PrimeNet

2⁵⁸

0.0175

62.0690%

10000

180000

0.0018

2.8620%

0.0193

63.1546%

1.0856%

GPU72

2⁶²

0.2798

64.5161%

11000

160000

0.0018

1.5710%

0.2817

65.0736%

0.5574%

Difference

+13.2544

+2.6481%

+489000

+14840000

+0.1212

+3.6098%

+13.3755

+3.7918%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2195467	93138994614712673527	20	66.336	21211658980689 3 × 997 × 7091828479	2008-12-23	997	7091828479	11.072	36.837	68.801

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2195467

93138994614712673527

66.336

21211658980689
3 × 997 × 7091828479

2008-12-23

997

7091828479

11.072

36.837

68.801

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2016-03-29T11:23:54	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.181%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.455 GHz-days
Estimated T-Level:	0.850

Digits	B1	Curves	Complete	FacMiss
20	11000	17 / 100	0.170	84.294%
25	50000	17 / 280	0.061	94.099%

New Calculation Method

Total ECM effort:	1.455 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.654	52.004%
25	50000	0.060	94.130%
30	250000	0.004	99.619%

ECM Summary

B1	B2	factor	curves	GHz-days
		93138994614712673527	1	0.00000e+0
50000	5000000		17	1.455

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-23T17:28:00	alan145	Bear4			93138994614712673527	66.336		1		1	-
2018-09-10T05:39:59	Oliver Kruse	ECM-HTC	50000	5000000						3	0.257
2022-05-13T21:09:17	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.599
2022-07-07T23:10:48	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.599

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	3E605A5D4213A2D6	0.144

date

userid

compid

res64

spent (GHz-days)

1999-02-14T00:00:00

ANONYMOUS

v4_computers

3E605A5D4213A2D6

0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T17:16:56

Oliver Kruse

93138994614712673527

07FAC8218420C9__

2017-11-19T18:53:29

kkmrkkblmbrbk

c4.xlarge

93138994614712673527

07FAC8218420C9__

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 = 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

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