Python 'for' loop is memory inefficient

Dr. Phillip M. Feldman pfeldman at
Sat Aug 15 03:25:45 CEST 2009

I wrote the following correct but inefficient test of primality for purposes
of demonstrating that the simplest algorithm is often not the most
efficient.  But, when I try to run the following code with a value of n that
is large enough to produce a significant amount of running time, I get an
out-of-memory error!

def is_prime(n):
   for j in range(2,n):
      if (n % j) == 0: return False
   return True

It seems as though Python is actually expanding range(2,n) into a list of
numbers, even though this is incredibly wasteful of memory. There should be
a looping mechanism that generates the index variable values incrementally
as they are needed.
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