Solved problem 41.

ipython/EulerProblem041.ipynb

@@ -13,6 +13,8 @@
     "collapsed": true
    },
    "source": [
+    "[https://projecteuler.net/problem=41]\n",
+    "\n",
     "We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.\n",
     "\n",
     "What is the largest n-digit pandigital prime that exists?"
@@ -20,16 +22,78 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 49,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "def expmod(base, exp, m):\n",
+    "    if exp == 0:\n",
+    "        return 1\n",
+    "    if (exp % 2 == 0):\n",
+    "        return (expmod(base, exp // 2, m) ** 2 % m)\n",
+    "    return (base * expmod(base, exp - 1, m) % m)\n",
+    "    \n",
+    "def expmod_naiv(base, exp, m):\n",
+    "    return base ** exp % m\n",
+    "\n",
+    "def fermat_test(n):\n",
+    "    a = n - 3\n",
+    "    return expmod(a, n, n) == a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert(expmod(2, 100000, 2143) == expmod_naiv(2, 100000, 2143))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert(fermat_test(2143))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "7652413\n"
+     ]
+    }
+   ],
+   "source": [
+    "import itertools\n",
+    "\n",
+    "for pandigital in itertools.permutations(\"7654321\"):\n",
+    "    p = int(\"\".join(pandigital))\n",
+    "    if fermat_test(p):\n",
+    "        s = p\n",
+    "        break\n",
+    "        \n",
+    "print(s)\n",
+    "assert(s == 7652413)"
+   ]
   }
  ],
  "metadata": {
-  "completion_date": "",
+  "completion_date": "Wed, 19 Dec 2018, 20:14",
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python3.6",
@@ -49,7 +113,9 @@
   },
   "tags": [
    "pandigital",
-   "prime"
+   "prime",
+   "fermat",
+   "test"
   ]
  },
  "nbformat": 4,