Why should the size of a hash table’s array be a prime number to minimize collisions?

Let’s say the index of a hash table’s array is given by i = h(key) % table_size.

If table_size is 10, then many numbers are divisible by 10, e.g., 10, 20, 30, 40. This means that the index i will more often be 0, increasing the probability of collisions.

However, if table_size is a prime number, then only a few values of h(key) will result in 0—specifically, multiples of the prime number and 0. As a result, the probability of a collision is lower.