Problem 51

51.py

@@ -0,0 +1,27 @@
+import itertools as it
+import gmpy2
+
+length  = 6
+repeats = 3
+permupattern = [0, 0, 0, 1, 1, 1]
+familysize = 8
+patterns = list(set(list(it.permutations(permupattern, length))))
+digits   = list(it.product(range(0, 10), repeat=length-repeats))
+
+for pattern in patterns:
+    for digit in digits:
+        family = []
+        for i in range(0, 10):
+            numlist = []
+            count = 0
+            for p in pattern:
+                if p:
+                    numlist.append(i)
+                else:
+                    numlist.append(digit[count])
+                    count += 1
+            num = int(''.join(map(str, numlist)))
+            if len(str(num)) == length:
+                family.append(num)
+        if family and len(filter(lambda n: gmpy2.is_prime(n), family)) == familysize: 
+            print family