Python large random integers and the precision of the Mersenne Twister

53 bits is not an inherent limit in the generator, it is the amount that Python returns when you request a float, since floats have 53 bits of precision.

You can get random integers directly using stuff like random.getrandbits.

In more detail, the Mersenne Twister used in CPython generates 32 bits at a time. The module code calls this twice and combines the results to generate a 53 bit float. If you call getrandbits, it will call the internal function as many times as necessary to generate k bits. The code for this can be found in here.

What Python does is generate 64 bits of randomness from calling the 32-bit version of MT19937 twice, but since that number is constrained to [0.0, 1.0) the result is constrained to 53 bits of precision (limitation of floating-point format).

Python random.py is capable of pulling bits from /dev/urandom or Windows CryptGenRandom (if supported), if you use the random.SystemRandom class. Otherwise, it generates larger numbers by pulling successive bits from repeated calls to MT19937.