Fastest Home Prime Generator What is a home prime?

For an example, take HP(4). First, find the prime factors. The prime factors of 4 (in numerical order from least to greatest, always) are 2, 2. Take those factors as a literal number. 2, 2 becomes 22. This process of factoring continues until you reach a prime number.

number    prime factors
4         2, 2
22        2, 11
211       211 is prime


Once you reach a prime number, the sequence ends. HP(4)=211. Here's a longer example, with 14:

number    prime factors
14        2, 7
27        3, 3, 3
333       3, 3, 37
3337      47, 71
4771      13, 367
13367     13367 is prime


Your challenge is to create a program that will calculate HP(x) given x, and do it as quickly as possible. You may use whatever resources you want, other than a list of known home primes.

Take note, these numbers become very large very fast. At x=8, HP(x) jumps all the way to 3331113965338635107. HP(49) has yet to be found.

Program speed will be tested on a Raspberry Pi 2, averaging the following inputs:

16
20
64
65
80


If you have a Raspberry Pi 2, time the program yourself, then average the times.
Mathematica, HP(80) in ~0.88s

NestWhile[
  FromDigits[
    Flatten[IntegerDigits /@ 
      ConstantArray @@@ FactorInteger[#]]] &amp;, #, CompositeQ] &amp;


Anonymous function. Takes a number as input and returns a number as output.