When is hash(n) == n in Python?

Question

I\'ve been playing with Python\'s hash function. For small integers, it appears hash(n) == n always. However this does not extend to large numbers:

Answer 1

2305843009213693951 is 2^61 - 1. It's the largest Mersenne prime that fits into 64 bits.

If you have to make a hash just by taking the value mod some number, then a large Mersenne prime is a good choice -- it's easy to compute and ensures an even distribution of possibilities. (Although I personally would never make a hash this way)

It's especially convenient to compute the modulus for floating point numbers. They have an exponential component that multiplies the whole number by 2^x. Since 2^61 = 1 mod 2^61-1, you only need to consider the (exponent) mod 61.

See: https://en.wikipedia.org/wiki/Mersenne_prime