M6235739 Mersenne number exponent details

Residue

Status

L-L

4548496AD8DD46E4

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	4.7651	65.6716%	115000	2271250	0.0597	3.2900%	4.8248	66.8010%	1.1294%
PrimeNet	2⁶²	0.0985	62.9032%	26000	600000	0.0147	3.3507%	0.1132	64.1462%	1.2430%
GPU72	2⁶⁶	2.3684	65.1515%	40000	900000	0.0223	2.4326%	2.3907	65.9992%	0.8477%
Difference	+1	+2.3967	+0.5201%	+75000	+1371250	+0.0374	+0.8574%	+2.4342	+0.8018%	+0.8018%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.7651

65.6716%

115000

2271250

0.0597

3.2900%

4.8248

66.8010%

1.1294%

PrimeNet

2⁶²

0.0985

62.9032%

26000

600000

0.0147

3.3507%

0.1132

64.1462%

1.2430%

GPU72

2⁶⁶

2.3684

65.1515%

40000

900000

0.0223

2.4326%

2.3907

65.9992%

0.8477%

Difference

+2.3967

+0.5201%

+75000

+1371250

+0.0374

+0.8574%

+2.4342

+0.8018%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6235739	116800657262651086743553	24	76.628	9365422226832384 2¹⁰ × 3 × 3048640047797	2011-09-28	1024	3048640047797	3,773.8	42,683	79,719

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6235739

116800657262651086743553

76.628

9365422226832384
2¹⁰ × 3 × 3048640047797

2011-09-28

1024

3048640047797

3,773.8

42,683

79,719

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	ANONYMOUS	v4_computers	20000	75000		-		-	-	0.006	-	-	0.814%
2011-05-15T20:59:00	markr	Manual testing	115000	2271250		-		-	-	0.060	-	-	3.290%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.049	-	-
1998-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.099	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		116800657262651086743553	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-09-28T09:07:00	JimBa	Dell			116800657262651086743553	76.628		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	4548496AD8DD46E4	1.105
2001-02-04T00:00:00	ANONYMOUS	v4_computers	4548496AD8DD46E4	1.105

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-13T18:30:00

kkmrkkblmbrbk

c4.xlarge

73BB341BBA73B3__

2018-10-01T20:36:15

Nesowa

Laptop

116800657262651086743553

73BB341BBA73B3__

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 = 115000, B2 = 2271250 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 20000, B2 = 75000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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