Luke 2

luke2

void Main()
{
	var result = FindNumber(9);
	Console.WriteLine (result);
}

public int FindNumber(int n){
	var seed = n * (int) Math.Pow(10,n-1);
	return FindNumber(seed, n-1, n, new Primes());
}

public int FindNumber(int seed, int position, int lastDigit, Primes primes){
	if(position < 0) return seed;
	foreach (var element in primes.BeginningWith(lastDigit))
	{
		var p = primes.Clone();
		var newSeed = AddLastDigitAt(seed,element,position);
		p.Remove(element);
		var result = FindNumber(newSeed,position-1,element % 10, p);
		if(result > 0) return result;
	}
	return 0;
}


public int AddLastDigitAt(int seed, int numberToAdd, int pos){
	var digit = numberToAdd % 10;
	return seed + digit * (int) Math.Pow(10,pos-1);
}

public class Primes
{
	List<int> _primes;
	public Primes():this(new List<int>{11  ,  13  ,  17  ,  19  ,  23  ,  29  ,  31  ,  37  ,  41  ,  43  ,  47  ,  53  ,  59  ,  61  ,  67  ,  71  ,  73  ,  79  ,  83  ,  89  ,  97 })
	{
	}
	
	private Primes(List<int> primes)
	{
		_primes = primes;
	}
	
	public Primes Clone(){
		return new Primes(_primes.ToList());
	}
	
	public void Remove(int d){
		_primes.Remove(d);
	}
	
	public IEnumerable<int> BeginningWith(int d){
		return _primes.OrderBy (x => x).Where (x => (x-x%10)/10 == d);
	}
}