Question

What is the upper bound of the range() function and how can I extend it, or alternately what’s the best way to do this:

for i in range(1,600851475143):

Answer 1

range(1, 600851475143) wants to generate a very large list in memory, and you’ll get an out of memory error. To save memory, use xrange instead of range. Unfortunately, xrange doesn’t work with large numbers (it’s an implementation restriction) Example (raises OverflowError):

for i in xrange(1, 600851475143):
  print i

You can have large minimum or maximum values in your interval with range, if their difference is small. Example:

x = 1 << 200
print list(xrange(x, x + 3))

Output:

[1606938044258990275541962092341162602522202993782792835301376L, 1606938044258990275541962092341162602522202993782792835301377L, 1606938044258990275541962092341162602522202993782792835301378L]

A fancy solution to your original for loop problem:

def bigrange(a, b = None):
  if b is None:
    b = a
    a = 0
  while a < b:
    yield a
    a += 1

for i in bigrange(1, 600851475143):
  print i

A less fancy solution, which works even if you have continue in the loop body:

i = 1 - 1
while i < 600851475143 - 1:
  i += 1
  print i