M4950287 Mersenne number exponent details

Residue

Status

L-L

1CAF8F85FEB4B859

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	6.0025	65.6716%	1200000	39750000	0.6633	7.3626%	6.6658	68.1991%	2.5275%
PrimeNet	2⁶¹	0.0621	62.2951%	22000	450000	0.0091	3.3077%	0.0712	63.5423%	1.2472%
GPU72	2⁶⁵	1.4738	64.6154%	34000	700000	0.0141	2.4119%	1.4879	65.4688%	0.8535%
Difference	+2	+4.5287	+1.0563%	+1166000	+39050000	+0.6492	+4.9506%	+5.1779	+2.7303%	+2.7303%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.0025

65.6716%

1200000

39750000

0.6633

7.3626%

6.6658

68.1991%

2.5275%

PrimeNet

2⁶¹

0.0621

62.2951%

22000

450000

0.0091

3.3077%

0.0712

63.5423%

1.2472%

GPU72

2⁶⁵

1.4738

64.6154%

34000

700000

0.0141

2.4119%

1.4879

65.4688%

0.8535%

Difference

+4.5287

+1.0563%

+1166000

+39050000

+0.6492

+4.9506%

+5.1779

+2.7303%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4950287	1828768745440735830900984469921	31	100.529	184713406055117191276080 2⁴ × 3 × 5 × 7 × 17 × 41 × 97 × 859 × 587551 × 3222151	2014-12-28	587551	3222151	3.301e+10	0.1469	0.2403

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4950287

1828768745440735830900984469921

100.529

184713406055117191276080
2⁴ × 3 × 5 × 7 × 17 × 41 × 97 × 859 × 587551 × 3222151

2014-12-28

587551

3222151

3.301e+10

0.1469

0.2403

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-05-24T00:00:00	estrand	v4_computers	25000	218750		-		-	-	0.007	-	-	1.219%
2011-07-20T18:30:00	harlee	P4_2600	60000	960000		-		-	-	0.022	-	-	2.291%
2014-12-28T13:48:00	mikr	MSI	1200000	39750000	12		1828768745440735830900984469921	31	100.529	0.663	1.372	1.327	7.363%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-12-31T22:59:00	markr	rmst	2⁶¹	2⁶²		-	-	0.062	-	-
2011-08-27T22:56:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.322	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.261 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.261 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.261

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-05-08T19:10:00	alan145	Bear4	50000	5000000						3	0.631
2014-04-02T11:10:00	Tha	Riet-Ubuntu	50000	5000000						3	0.631

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-09-27T00:00:00	ANONYMOUS	v4_computers	1CAF8F85FEB4B859	0.686
2000-06-11T00:00:00	estrand	v4_computers	1CAF8F85FEB4B859	0.686

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:41:11

kkmrkkblmbrbk

Manual testing

1828768745440735830900984469921

CFE7A6E433052B__

2018-04-16T03:30:13

ATH

ec2-PRPCFDC

1828768745440735830900984469921

CFE7A6E433052B__

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 = 1200000, B2 = 39750000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 60000, B2 = 960000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 25000, B2 = 218750 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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