## Posts Tagged ‘factoring’

### Programming Praxis – Two Factoring Games

February 18, 2011

In today’s Programming Praxis exercise, our goal is to implement two algorithms related to prime factors; one to calculate the home prime of a number and one to generate the Euclid-Mullin sequence. Let’s get started, shall we?

Some imports:

```import Data.List
import Data.Numbers.Primes
```

To calculate the home prime we repeatedly concatenate the digits of the prime factors until the number is prime.

```homePrime :: Integer -> Integer
homePrime = head . filter isPrime .
iterate (read . concatMap show . primeFactors)
```

The Eulic-Mullin sequence can be written as a basic unfold.

```euclidMullin :: [Integer]
euclidMullin = unfoldr (\p -> let a = head (primeFactors \$ p + 1)
in  Just (a, p * a)) 1
```

Naturally, we need to test if we did everything correctly:

```main :: IO ()
main = do print \$ homePrime 99 == 71143
print \$ take 10 euclidMullin ==
[2,3,7,43,13,53,5,6221671,38709183810571,139]
```

Looks like everything is working properly.