Solve problem 118.

python/e118.py

@@ -0,0 +1,45 @@
+from itertools import combinations, permutations
+from lib_prime import is_prime_rabin_miller as is_prime
+
+
+def as_number(xs) -> int:
+    return int("".join(map(str, xs)))
+
+
+def list_diff(xs, ys):
+    xs = list(xs)
+    for y in ys:
+        xs.remove(y)
+    return xs
+
+
+def combs(xs, size):
+    return sorted([p
+        for cs in combinations(xs, size)
+        for p in permutations(cs)])
+
+
+def count(min_set_size: int, min_num: int, remaining: list[int]) -> int:
+    if not remaining:
+        return 1
+
+    result = 0
+    # There are no pandigital primes with 9 digits, so we only check till 8.
+    for set_size in range(min_set_size, 9):
+        for subset in combs(remaining, set_size):
+            n = as_number(subset)
+            if n > min_num and is_prime(n):
+                new_remaining = list_diff(remaining, subset)
+                result += count(set_size, n, new_remaining)
+    return result
+
+
+def euler_118():
+    return count(1, 0, [1, 2, 3, 4, 5, 6, 7, 8, 9])
+
+
+if __name__ == "__main__":
+    solution = euler_118()
+    print("e118.py: " + str(solution))
+    assert(solution == 44680)
+

python/lib_prime.py

@@ -70,6 +70,9 @@ def is_prime_rabin_miller(number):
     """ Rabin-Miller Primality Test """
     witnesses = [2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53]
 
+    if number < 2:
+        return False
+
     if number in witnesses:
         return True