Why should hash functions use a prime number modulus?

Question

A long time ago, I bought a data structures book off the bargain table for $1.25. In it, the explanation for a hashing function said that it should ultimately mod by a prime number because of "the nature of math".What do you expect from a $1.25 book?Anyway, I've had years to think about the nature of math, and still can't figure it out.Is the distribution of numbers truly more even when there are a prime number of buckets? Or is this an old programmer's tale that everyone accepts because everybody *else* accepts it?

Answer 1

Honestly have never head of such a thing...

Ex. a telephone registry, phone book, or roll call, will have

26 buckets, 1 for each letter in the alphabet.

26 is not prime