M4253429 Mersenne number exponent details

Residue

Status

L-L

ACF857589371CA67

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	6.9859	65.6716%	50000	762500	0.0161	2.0241%	7.0019	66.3665%	0.6948%
PrimeNet	2⁶¹	0.0722	62.2951%	18000	360000	0.0066	2.9203%	0.0788	63.3962%	1.1011%
GPU72	2⁶⁵	1.7153	64.6154%	24000	450000	0.0085	1.9236%	1.7238	65.2961%	0.6807%
Difference	+2	+5.2706	+1.0563%	+26000	+312500	+0.0075	+0.1005%	+5.2781	+1.0704%	+1.0704%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.9859

65.6716%

50000

762500

0.0161

2.0241%

7.0019

66.3665%

0.6948%

PrimeNet

2⁶¹

0.0722

62.2951%

18000

360000

0.0066

2.9203%

0.0788

63.3962%

1.1011%

GPU72

2⁶⁵

1.7153

64.6154%

24000

450000

0.0085

1.9236%

1.7238

65.2961%

0.6807%

Difference

+5.2706

+1.0563%

+26000

+312500

+0.0075

+0.1005%

+5.2781

+1.0704%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4253429	51294930425738343649	20	65.475	6029832686256 2⁴ × 3³ × 17 × 211 × 3891259	2013-02-18	211	3891259	1.8887	0.0384	0.0716

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4253429

51294930425738343649

65.475

6029832686256
2⁴ × 3³ × 17 × 211 × 3891259

2013-02-18

211

3891259

1.8887

0.0384

0.0716

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-01T05:06:00	Carsten Kossendey	durandal	25000	337500		-		-	-	0.008	-	-	1.354%
2011-08-18T18:25:00	Squeeky_Squirrel	T7500_2200	50000	762500		-		-	-	0.016	-	-	2.024%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.036	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.072	-	-
2011-01-07T16:40:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.072	-	-
2012-01-31T04:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.375	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.547 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:	0.547 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		51294930425738343649	1	0.00000e+0
50000	5000000		3	0.547

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-02T18:12:00	Wojciech Florek	LBwin	50000	5000000						3	0.547
2013-02-18T02:27:00	Xyzzy	J			51294930425738343649	65.475		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-01T00:00:00	ANONYMOUS	v4_computers	ACF857589371CA67	0.530
2000-04-19T00:00:00	S10747	v4_computers	ACF857589371CA67	0.530

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T16:58:09

kkmrkkblmbrbk

Manual testing

51294930425738343649

463971B22FBEC0__

2018-01-23T22:47:13

Oliver Kruse

GTX-2

51294930425738343649

463971B22FBEC0__

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 = 50000, B2 = 762500 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 25000, B2 = 337500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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