Solves problem 41.

Would really need some decorators to spped up the process and get it
prettier though.

README.markdown

@@ -48,6 +48,7 @@ Should be used in order to help future reuse of code :)
 36 - Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. - 0.933 <br />
 37 - Find the sum of all eleven primes that are both truncatable from left to right and right to left. < 1 min <br />
 39 - If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p <= 1000, has the most solutions? - 1min<br />
+41 - What is the largest n-digit pandigital prime that exists? < 5 min <br />
 42 - Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words? - < 1 sec <br />
 45 - Find the next triangle number that is also pentagonal and hexagonal. - < 1 sec <br /> 
 48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000. - 0.053 <br />
@@ -60,7 +61,6 @@ Should be used in order to help future reuse of code :)
 26 - Find the value of d < 1000 for which 1/d contains the longest recurring cycle. <br />
 33 - Discover all the fractions with an unorthodox cancelling method. <br />
 38 - What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? <br />
-41 - What is the largest n-digit pandigital prime that exists? <br />
 97 - Find the last ten digits of the non-Mersenne prime: 28433 × 2^7830457 + 1.
 
 **WARNING : Spoil inside for those who want to solve problems by themselves :)**

e_41.py

@@ -10,6 +10,81 @@ We shall say that an n-digit number is pandigital if it makes use of all the dig
 What is the largest n-digit pandigital prime that exists?
 ''' 
 
+val = 123456789 # all numbers to create the biggest pandigital number
+def is_prime(value):
+    """
+    Returns True or False depending whether value is prime or not. 
+    """
+    start = 2
+    while (start <= value / 2):
+        if value % start == 0 :
+            return False
+        else : 
+            start += 1
+    return True
+
+# I could use a decorator to remove trivial non primes here
+def all_permutations(seq):
+    """permutates a sequence and returns a list of the permutations"""
+    if not seq:
+        return [seq]  # is an empty sequence
+    else:
+        temp = []
+        for k in range(len(seq)):
+            part = seq[:k] + seq[k+1:]
+            for m in all_permutations(part):
+                temp.append(seq[k:k+1] + m)
+        return temp
+
+def divisible_by_2(val):
+    """
+    Returns True if val contains an even number (ex : 998)
+    """
+    return ((val % 2) == 0)
+
+def divisible_by_5(val):
+    """
+    Returns True if any circular permutation of val is divisible by  (ex : 907)
+    """    
+    return (str(5) == str(val)[-1])
+    
+def divisible_by_3(val):
+    """
+    Returns True if any circular permutation of val is divisible by 3 (ex : 12)
+    """    
+    temp = sum([int(p) for p in str(val)])
+    if len(str(temp)) > 1:
+        divisible_by_3(temp)
+    else:
+        return ((temp % 3) == 0)
+
+def check_easy_out(pelist):
+    """
+    Returns the number of circular primes below max_val
+    
+    TODO : do this while creating all the permutations !
+    """
+    pred = list(pelist)
+    for p in pelist:
+        if p > 11: # my filter does not work for values under 10
+            if (divisible_by_2(p) or divisible_by_5(p) or divisible_by_3(p)): 
+                pred.remove(p)    
+    return pred
+
+def biggest_pandigital():
+    """
+    Returns the biggest pandigital prime number
+    """
+    for n in range(9): # from 0 to 9 numbers removed of max pand number
+        print " n : %d" %(n)
+        root = str(val)[:len(str(val)) -n]
+        perms = [ int(p) for p in all_permutations(root)]
+        perms = check_easy_out(perms)
+        perms.sort(reverse=True)
+        for p in perms : 
+            if is_prime(p):
+                return p
+        
+    return -1 # problem
 if __name__ == '__main__':
-    print 1
-    #print "Answer : %d " % (last_ten())
+    print "Answer : %d " % (biggest_pandigital())