General advice and guidelines on how to properly override object.GetHashCode()

Question

According to MSDN, a hash function must have the following properties:

1. If two objects compare as equal, the GetHashCode method for each object m

Answer 1

What are those magic numbers often seen in GetHashCode implementations?

They are prime numbers. Prime numbers are used for creating hash codes because prime number maximize the usage of the hash code space.

Specifically, start with the small prime number 3, and consider only the low-order nybbles of the results:

• 3 * 1 = 3 = 3(mod 8) = 0011
• 3 * 2 = 6 = 6(mod 8) = 1010
• 3 * 3 = 9 = 1(mod 8) = 0001
• 3 * 4 = 12 = 4(mod 8) = 1000
• 3 * 5 = 15 = 7(mod 8) = 1111
• 3 * 6 = 18 = 2(mod 8) = 0010
• 3 * 7 = 21 = 5(mod 8) = 1001
• 3 * 8 = 24 = 0(mod 8) = 0000
• 3 * 9 = 27 = 3(mod 8) = 0011

And we start over. But you'll notice that successive multiples of our prime generated every possible permutation of bits in our nybble before starting to repeat. We can get the same effect with any prime number and any number of bits, which makes prime numbers optimal for generating near-random hash codes. The reason we usually see larger primes instead of small primes like 3 in the example above is that, for greater numbers of bits in our hash code, the results obtained from using a small prime are not even pseudo-random - they're simply an increasing sequence until an overflow is encountered. For optimal randomness, a prime number that results in overflow for fairly small coefficients should be used, unless you can guarantee that your coefficients will not be small.

Related links:

• Why is ‘397’ used for ReSharper GetHashCode override?