Problem Statement

In number theory, the home prime HP(n) of an integer n greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The traditional notation has the prefix "HP" and a postfix count of the number of iterations until the home prime is found (if the count is greater than 0), for instance HP4(2) === HP22(1) === 211 is the same as saying the home prime of 4 needs 2 iterations and is the same as the home prime of 22 which needs 1 iteration, and (both) resolve to 211, a prime. Prime numbers are their own home prime; So: If the integer obtained by concatenating increasing prime factors is not prime, iterate until you reach a prime number; the home prime.

Let's start with the solution:

for n in (2..20, 65) {

    var steps = []
    var orig = n

    for (var f = n.factor; true; f = n.factor) {
        steps << f
        n = Num(f.join)
        break if n.is_prime
    }

    say ("HP(#{orig}) = ", steps.map { .join('_') }.join(' -> '))
}