Why use a prime number in hashCode?

Question

I was just wondering why is that primes are used in a class's hashCode() method? For example, when using Eclipse to generate my hashCode() method there is always the prime number 31 used:

public int hashCode() {
     final int prime = 31;
     //...
}

References:

Here is a good primer on Hashcode and article on how hashing works that I found (C# but the concepts are transferrable): Eric Lippert's Guidelines and rules for GetHashCode()

Answer 1

Prime numbers are chosen to best distribute data among hash buckets. If the distribution of inputs is random and evenly spread, then the choice of the hash code/modulus does not matter. It only has an impact when there is a certain pattern to the inputs.

This is often the case when dealing with memory locations. For example, all 32-bit integers are aligned to addresses divisible by 4. Check out the table below to visualize the effects of using a prime vs. non-prime modulus:

Input       Modulo 8    Modulo 7
0           0           0
4           4           4
8           0           1
12          4           5
16          0           2
20          4           6
24          0           3
28          4           0

Notice the almost-perfect distribution when using a prime modulus vs. a non-prime modulus.

However, although the above example is largely contrived, the general principle is that when dealing with a pattern of inputs, using a prime number modulus will yield the best distribution.