Solved 47

problem47.py

@@ -0,0 +1,28 @@
+#!/usr/bin/env python
+from __future__ import division
+from utils import primes_until
+
+primes = list(primes_until(10000))
+
+def distinct(n, frm=0):
+    for i, p in enumerate(primes[frm:]):
+        div = n / p
+
+        if div < 2:
+            break
+
+        if div.is_integer():
+            others = set([int(div)]) if div in primes[i:] else distinct(div, i)
+
+            if others:
+                return others | set([p])
+
+n = N = 4
+counter = 0
+
+while counter != N:
+    factors = distinct(n)
+    counter = counter + 1 if factors and len(factors) == N else 0
+    n += 1
+
+print n - N