Why multiply by a prime before xoring in many GetHashCode Implementations?

Question

I understand that multiplication by a large number before xoring should help with badly distributed operands but why should the multiplier be a prime?

Answer 1

Consider the simplest multiplication: x2.

It is equivalent to a left-bitshift. In other words, it really didn't "randomize" the data, it just shifted it over.

Same with x4, or any power of two. The original data is intact, just shifted.

Now, multiplication by other numbers (non-powers of two) are not as obvious, but still have the same problem, more or less. The original data is intact, or trivially transformed. (eg. x5 is the same as left-bitshift two places, then add on the original data).

The point of GetHashCode is to essentially distribute the data as randomly as possible. Multiplying by a prime number guarantees that the answer won't be a simpler transform like bit-shifting or adding a number to itself.