TASK 1: Perrin Prime

The Perrin sequence is defined to start with [3, 0, 2]; after that, term
N is the sum of terms N-2 and N-3. (So it continues 3, 2, 5, 5, 7, ....)

A Perrin prime is a number in the Perrin sequence which is also a prime number.

Calculate the first 13 Perrin Primes.

f(13) = [2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977]

MY NOTES: ok, sounds relatively easy, except that the 12th and 13th PP are
enormous.  I normally reusing my old favourite MakePrimes.pm (Sieve of
Eratosthenes based) but this time I think I'll have to do it the old
fashioned "try all factors up to sqrt()" approach.


Task 2: Home Prime

You are given an integer greater than 1.

Write a script to find the home prime of the given number.

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.

Further information can be found on Wikipedia

https://en.wikipedia.org/wiki/Home_prime

Example

As given in the Wikipedia page:

HP(10) = 773, as 10 factors as 2x5 yielding HP10(1) = 25, 25 factors
as 5x5 yielding HP10(2) = HP25(1) = 55, 55 = 5x11 implies HP10(3)
= HP25(2) = HP55(1) = 511, and 511 = 7x73 gives HP10(4) = HP25(3) =
HP55(2) = HP511(1) = 773, a prime number.

MY NOTES: Ok, yet another prime variant.  I'll have a go, but I note that
the numbers get enormous, to the point where it's not even known if HP(49)
can be calculated.  Again can't use MakePrimes.pm..