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Related Pages
Related Symbols
FactorInteger
Related Categories
Computer Science
Speed of Factoring
Example Notebook
Open in Cloud
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Factor numbers
n
1
0
for n up to 50, measuring how long it takes:
I
n
[
1
]
:
=
t
i
m
i
n
g
d
a
t
a
=
T
a
b
l
e
[
A
b
s
o
l
u
t
e
T
i
m
i
n
g
[
F
a
c
t
o
r
I
n
t
e
g
e
r
[
R
a
n
d
o
m
I
n
t
e
g
e
r
[
1
0
^
n
]
]
]
,
{
n
,
5
0
}
]
;
S
h
o
r
t
[
t
i
m
i
n
g
d
a
t
a
,
3
]
O
u
t
[
1
]
/
/
S
h
o
r
t
=
{
{
0
.
0
0
0
0
1
5
,
{
{
3
,
1
}
}
}
,
{
6
.
×
-
6
1
0
,
{
{
2
,
5
}
}
}
,
{
7
.
×
-
6
1
0
,
{
{
2
,
4
}
,
{
3
,
1
}
,
{
1
3
,
1
}
}
}
,
4
5
,
{
0
.
0
0
5
0
6
,
{
{
2
,
2
}
,
{
6
7
,
1
}
,
{
3
9
2
1
4
5
1
,
1
}
,
{
7
7
0
2
3
1
3
7
9
1
4
4
6
5
8
1
1
2
4
3
7
7
1
2
3
1
6
7
3
5
2
7
1
0
2
7
7
5
5
1
,
1
}
}
}
,
{
0
.
7
5
7
0
6
,
{
{
2
,
4
}
,
{
3
,
1
}
,
{
5
,
1
}
,
{
2
3
,
1
}
,
{
4
4
7
0
9
3
0
7
9
6
1
5
3
7
,
1
}
,
{
1
8
7
0
1
6
7
1
2
9
2
2
9
1
4
2
6
7
5
2
6
7
7
0
3
0
1
8
8
5
9
2
1
,
1
}
}
}
}
Get the list of times:
I
n
[
2
]
:
=
F
i
r
s
t
/
@
t
i
m
i
n
g
d
a
t
a
O
u
t
[
2
]
=
{
0
.
0
0
0
0
1
5
,
6
.
×
-
6
1
0
,
7
.
×
-
6
1
0
,
4
.
×
-
6
1
0
,
4
.
×
-
6
1
0
,
5
.
×
-
6
1
0
,
4
.
×
-
6
1
0
,
8
.
×
-
6
1
0
,
6
.
×
-
6
1
0
,
0
.
0
0
0
0
1
,
9
.
×
-
6
1
0
,
0
.
0
0
0
0
9
,
0
.
0
0
0
0
1
4
,
0
.
0
0
0
0
9
1
,
0
.
0
0
0
0
2
1
,
0
.
0
0
0
0
9
4
,
0
.
0
0
0
0
9
9
,
0
.
0
0
0
9
0
9
,
0
.
0
0
2
1
,
0
.
0
0
0
0
4
3
,
0
.
0
0
0
1
2
1
,
0
.
0
0
0
1
4
5
,
0
.
0
0
0
4
7
2
,
0
.
0
0
5
0
1
4
,
0
.
0
0
0
1
4
3
,
0
.
0
0
0
6
6
3
,
0
.
0
0
7
1
9
7
,
0
.
0
0
0
3
1
5
,
0
.
0
0
2
1
0
3
,
0
.
0
0
0
3
4
,
0
.
0
0
6
5
2
2
,
0
.
0
0
0
3
9
9
,
0
.
0
0
0
3
8
1
,
0
.
0
0
0
3
4
3
,
0
.
0
1
0
9
6
,
0
.
0
1
1
3
8
4
,
0
.
0
4
6
2
5
1
,
0
.
0
0
0
2
9
1
,
0
.
1
0
5
3
3
5
,
0
.
0
0
0
3
4
3
,
0
.
0
0
6
1
7
5
,
0
.
0
0
9
7
4
1
,
0
.
0
2
1
1
0
2
,
0
.
4
2
4
4
5
6
,
0
.
2
8
7
7
0
5
,
0
.
0
6
9
2
8
9
,
0
.
5
6
6
1
4
7
,
0
.
7
7
8
6
1
4
,
0
.
0
0
5
0
6
,
0
.
7
5
7
0
6
}
Make a log plot:
I
n
[
3
]
:
=
L
i
s
t
L
o
g
P
l
o
t
[
%
,
J
o
i
n
e
d
T
r
u
e
]
O
u
t
[
3
]
=
There are many fluctuations, but the trend is a linear increase on the log plot, corresponding to an exponential increase of the underlying data.
See Also
FactorGraph
LargestPrimeFactor
EvaluationTiming
Related Symbols
FactorInteger
Publisher Information
Contributed by:
Stephen Wolfram
