Maximum and Minimum values for ints

Python 3

In Python 3, this question doesn't apply. The plain int type is unbounded.

However, you might actually be looking for information about the current interpreter's word size, which will be the same as the machine's word size in most cases. That information is still available in Python 3 as sys.maxsize, which is the maximum value representable by a signed word. Equivalently, it's the size of the largest possible list or in-memory sequence.

Generally, the maximum value representable by an unsigned word will be sys.maxsize * 2 + 1, and the number of bits in a word will be math.log2(sys.maxsize * 2 + 2). See this answer for more information.

Python 2

In Python 2, the maximum value for plain int values is available as sys.maxint:

>>> sys.maxint  # on my system, 2**63-1
9223372036854775807

You can calculate the minimum value with -sys.maxint - 1 as shown in the docs.

Python seamlessly switches from plain to long integers once you exceed this value. So most of the time, you won't need to know it.

If you just need a number that's bigger than all others, you can use

float('inf')

in similar fashion, a number smaller than all others:

float('-inf')

This works in both python 2 and 3.

The sys.maxint constant has been removed from Python 3.0 onward, instead use sys.maxsize.

Integers

• PEP 237: Essentially, long renamed to int. That is, there is only one built-in integral type, named int; but it behaves mostly like the old long type.

...

• The sys.maxint constant was removed, since there is no longer a limit to the value of integers. However, sys.maxsize can be used as an integer larger than any practical list or string index. It conforms to the implementation’s “natural” integer size and is typically the same as sys.maxint in previous releases on the same platform (assuming the same build options).

In Python 2, integers will automatically switch from a fixed-size int representation into a variable width long representation once you pass the value sys.maxint, which is either 2³¹ - 1 or 2⁶³ - 1 depending on your platform. Notice the L that gets appended here:

>>> 9223372036854775807
9223372036854775807
>>> 9223372036854775808
9223372036854775808L

From the Python 2.7 manual:

Numbers are created by numeric literals or as the result of built-in functions and operators. Unadorned integer literals (including binary, hex, and octal numbers) yield plain integers unless the value they denote is too large to be represented as a plain integer, in which case they yield a long integer. Integer literals with an 'L' or 'l' suffix yield long integers ('L' is preferred because 1l looks too much like eleven!).

Python tries very hard to pretend its integers are mathematical integers and are unbounded. It can, for instance, calculate a googol with ease:

>>> 10**100
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000L