The prime numbers ≥ 5 within a finite sequence of natural numbers can be found arithmetically by calculating all of the values of 6n-1 and 6n+1 that fall within the sequence and subtracting the composites given by (6n_1±1)(6n_2±1), where n is a natural number. For a given value of n_1, successive (6n_1-1)(6n_2+1), (6n_1-1)(6n_2-1) and (6n_1+1)(6n_2+1) composites occur at a regular interval, which increases by 36 from one value of n_1 to the next. When combined, these regular but different intervals create disorder in the sequences of 6n-1 and 6n+1 composites, which in turn creates the apparent randomness of the primes in the sequence of natural numbers. Furthermore, {(6n_1-1)(6n_2-1)} and {(6n_1+1)(6n_2+1)} numbers are subsets of 6n+1 composites whereas the only subset of the 6n-1 composites is {(6n_1-1)(6n_2+1)}. This creates a slight inequality in the proportions of composites and primes between the sets {6n-1} and {6n+1}, which otherwise have an equal number of members overall.