# 2009 is not a prime number. A python program to compute factors.

In my customary "Happy New Year" mail, I sent out a small note :

PS: Quiz : Is 2009 a prime number ? - Ans : No

Soon I started getting responses about that wisecrack of mine. The one that really stumped me came from a dear friend which said,

Enjoy the new year and happy computing. BTW is 200000000000000000000000000009 a prime number?

Soon enough found a piece of python code to find factors - Factor for Python which seemed to find all the factors for a number. Wasn't likely to work too fast, so quickly modified it to the following code which finds all the prime factors for a number. Here's the code

**Update:** The first version had a bug which did not show the largest factor. Has since been corrected.

```
"""
Get the factors for a number
(Note: Not optimised for tail recursion)
"""
def factor(n):
if n == 1: return [1]
i = 2
limit = n**0.5
while i <= limit:
if n % i == 0:
ret = factor(n/i)
ret.append(i)
return ret
i += 1
return [n]
if __name__ == "__main__":
import sys
for index in xrange(1,len(sys.argv)):
print "Factors for %s : %s" %(sys.argv[index], str(factor(int(sys.argv[index]))))
```

Quickly gave me the following output (used all of 26.2 seconds to get there) :

```
# python getfactors.py 200000000000000000000000000009
Factors for 200000000000000000000000000009 : [13430577524641L, 2094523, 89, 47, 47, 43, 29, 29]
```

And in case you are wondering what are the factors for 2009

```
# python getfactors.py 2009
Factors for 2009 : [41, 7, 7]
```

And which is the next year which is a prime number ?

```
# python getfactors.py 2011
Factors for 2011 : [2011]
```

Pretty playful hacking for 10 mins I thought.

**Update:** The code above was written in 10 mins, but it kept bothering me .. just wasn't idiomatic python. So once I got some time, I got back to it and decided to write a generator instead. The results obviously stay the same but the time came down from 26 seconds to 4.7 seconds. I of course threw in an additional optimisation which had nothing to do with a generator - basically the value of i no longer restarts from 2, it resumes with the last factor (the same that was yielded and moves on from there). Here's the new code implementing a generator.

```
"""
Generator for getting factors for a number
"""
def factor(n):
yield 1
i = 2
limit = n**0.5
while i <= limit:
if n % i == 0:
yield i
n = n / i
limit = n**0.5
else:
i += 1
if n > 1:
yield n
if __name__ == "__main__":
import sys
for index in xrange(1,len(sys.argv)):
print "Factors for %s : %s" %(sys.argv[index], [i for i in factor(int(sys.argv[index]))])
```