diff --git a/TTM4135.ipynb b/TTM4135.ipynb
index 26da398..da75faf 100644
--- a/TTM4135.ipynb
+++ b/TTM4135.ipynb
@@ -46,7 +46,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -245,14 +245,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1105 is composite\n"
+      "1105 is probable prime\n"
      ]
     }
    ],
@@ -283,21 +283,93 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "# Miller-Rabin\n",
-    "n = 137\n",
-    "k = 20\n",
+    "## Miller-Rabin\n",
+    "From https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test  \n",
+    "This test is not fooled by Charmichael numbers.\n",
     "\n",
+    "To test `n`, you choose different `a` values, and test if \n",
+    "\n",
+    "> $a^{d*2^i} \\equiv 1 \\pmod{n}$ for $i = (0, 1, 2, ... r)$\n",
+    "\n",
+    "If this happens, look at the congruence on the calculation just before you got `1`. If that value is not -1 (aka n-1), the value is composite aka not prime."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "168 = 21*2^3 = 168\n",
+      "65536 = 1*2^16 = 65536\n",
+      "\n",
+      "16127 is probably prime.\n",
+      "561 is composite.\n",
+      "2465 is composite.\n",
+      "65537 is probably prime.\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Miller-Rabin primality test\n",
+    "# This test is not fooled by Charmichael numbers.\n",
+    "\n",
+    "from math import log2, floor\n",
     "from random import randint\n",
-    "def miller_rabin(n):\n",
-    "    for O in range(k):\n",
-    "        d = n-1\n",
-    "        a = randint(2,n-2)\n",
-    "        x = (a**d) % "
+    "\n",
+    "def decompose_even_number(n):\n",
+    "    '''Find the values r and d such that n == d * 2**r.'''\n",
+    "    r = 0\n",
+    "    d = n\n",
+    "    for i in range(1, floor(log2(n)) + 1):\n",
+    "        if (d/2).is_integer():\n",
+    "            d = d/2\n",
+    "            r += 1\n",
+    "        else:\n",
+    "            break\n",
+    "    return (r, int(d))\n",
+    "\n",
+    "verbose = False  # Print during execution\n",
+    "\n",
+    "def miller_rabin_prime(n):\n",
+    "    ''':param n: should be odd, and n>3. No primes can be even, for obvious reasons.'''\n",
+    "    accuracy = 3  # How many different `a` to test\n",
+    "    r, d = decompose_even_number(n-1)  # n is odd, thus n-1 is even\n",
+    "    verbose and print(f\"Testing {n} a maximum of {accuracy} times...\")\n",
+    "    \n",
+    "    for _ in range(accuracy):\n",
+    "        try:\n",
+    "            a = randint(2, n-2)  # The \"witness\".  TODO: don't reuse a witness.\n",
+    "            verbose and print(f\"\\tTesting {n} with a={a}\")\n",
+    "\n",
+    "            x = (a**d) % n\n",
+    "            if x == 1 or x == n-1:\n",
+    "                verbose and print(f\"\\t({a}**{d})%{n} was 1 or -1 already!\")\n",
+    "                continue # This witness was immediately 1 or -1 (aka n-1), so it can't help us any more.\n",
+    "            for squaring in range(r-1):\n",
+    "                x = (x**2) % n\n",
+    "                verbose and print(f\"\\tx={x}\")\n",
+    "                if x == n-1:\n",
+    "                    raise Exception(\"Try next witness\")  # This witness can't help any more.\n",
+    "            return \"composite\" # The witness didnt uphold the criteria for a prime, so n is composite!\n",
+    "        except Exception as tryNext:\n",
+    "            continue\n",
+    "    return \"probably prime\"\n",
+    "    \n",
+    "s, d = decompose_even_number(168)\n",
+    "print(f\"168 = {d}*2^{s} = {d*(2**s)}\")\n",
+    "s, d = decompose_even_number(65536)\n",
+    "print(f\"65536 = {d}*2^{s} = {d*(2**s)}\")\n",
+    "print()\n",
+    "\n",
+    "for value in [16127, 561, 2465, 65537]:\n",
+    "    print(f\"{value} is {miller_rabin_prime(value)}.\")\n"
    ]
   },
   {
@@ -371,7 +443,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
@@ -428,7 +500,7 @@
     "print(f\"y = g^x mod p    ==>    {y} = {g}^{x} mod {p}\")\n",
     "\n",
     "# Don't run the test with big numbers!\n",
-    "if x < 10000: print(f\"Test: {disc_log_test(y,g,x,p)}\")"
+    "if x<10000: print(f\"Test: {disc_log_test(y,g,x,p)}\")"
    ]
   },
   {
@@ -446,13 +518,6 @@
     "- `P = D(C, K)`: Decryption function"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "code",
    "execution_count": 10,
@@ -501,5 +566,5 @@
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }