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?

Related:
Why should hash functions use a prime number modulus?

Close, but not quite a Duplicate:
Why does Java’s hashCode() in String use 31 as a multiplier?

Answer 1

There’s a good article on the Computing Life blog that discusses this topic in detail. It was originally posted as a response to the Java hashCode() question I linked to in the question. According to the article:

Primes are unique numbers. They are unique in that, the product of a prime with any other number has the best chance of being unique (not as unique as the prime itself of-course) due to the fact that a prime is used to compose it. This property is used in hashing functions.

Given a string “Samuel”, you can generate a unique hash by multiply each of the constituent digits or letters with a prime number and adding them up. This is why primes are used.

However using primes is an old technique. The key here to understand that as long as you can generate a sufficiently unique key you can move to other hashing techniques too. Go here for more on this topic about hashes without primes.