Problem 037

e037.py

@@ -0,0 +1,35 @@
+"""Find the sum of all eleven primes that are both truncatable from left to right and right to left.
+
+The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
+Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
+
+NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
+"""
+
+from e007 import is_prime, prime_generator
+
+def is_truncatable(prime):
+    if prime < 10:
+        return False
+    rtl = [int(str(prime)[:i]) for i in xrange(len(str(prime))) if i > 0 and i < len(str(prime))]
+    ltr = [int(str(prime)[i:]) for i in xrange(len(str(prime))) if i > 0 and i < len(str(prime))]
+    truncated = sorted(rtl + ltr, reverse=True)
+    for n in truncated:
+        if not is_prime(n):
+            return False
+    print 'OK', prime, rtl, ltr
+    return True
+
+def main():
+    truncatable = []
+    generator = prime_generator()
+    print 'Searching for truncatable primes...'
+    while len(truncatable) < 11:
+        prime = generator.next()
+        if is_truncatable(prime):
+            truncatable.append(prime)
+    print 'Found {0} truncatable primes'.format(len(truncatable))
+    print 'Sum:', sum(truncatable)
+
+if __name__ == '__main__':
+    main()