Did problem 11 in ipython.

ipython/EulerProblem010.ipynb

@@ -5,7 +5,150 @@
    "metadata": {},
    "source": [
     "# Euler Problem 10\n",
-    "\n"
+    "\n",
+    "The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\n",
+    "\n",
+    "Find the sum of all the primes below two million."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Okay, reuse prime generator from 7 and go."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "61.8695481220002\n",
+      "142913828922\n"
+     ]
+    }
+   ],
+   "source": [
+    "import timeit\n",
+    "\n",
+    "def is_prime(n, smaller_primes):\n",
+    "    for s in smaller_primes:\n",
+    "        if n % s == 0:\n",
+    "            return False\n",
+    "        if s * s > n:\n",
+    "            return True\n",
+    "    return True\n",
+    "\n",
+    "def prime_generator_function():\n",
+    "    primes = [2, 3, 5, 7]\n",
+    "    for p in primes:\n",
+    "        yield p\n",
+    "    while True:\n",
+    "        p += 2\n",
+    "        if is_prime(p, primes):\n",
+    "            primes.append(p)\n",
+    "            yield p\n",
+    "    \n",
+    "def brute_force(): \n",
+    "    ps = prime_generator_function()\n",
+    "    s = 0\n",
+    "    p = next(ps)\n",
+    "    while p < 2000000:\n",
+    "        s += p\n",
+    "        p = next(ps)\n",
+    "    return s\n",
+    "    \n",
+    "print(timeit.timeit(brute_force, number=10))\n",
+    "assert(brute_force() == 142913828922)\n",
+    "print(brute_force())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Okay, here it may actually be way smarter to use a sieve. We implent it because the old one was shitty. Okay, I am actually interested in the time difference. So we use the old one first and then implement the optimization."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def get_primes_smaller(number):\n",
+    "    primes = []\n",
+    "    prospects = [n for n in range(2, number)]\n",
+    "    while prospects:\n",
+    "        p = prospects[0]\n",
+    "        prospects = [x for x in prospects if x % p != 0]\n",
+    "        primes.append(p)\n",
+    "    return primes\n",
+    "\n",
+    "def brute_force():\n",
+    "    return sum(get_primes_smaller(2000000))\n",
+    "\n",
+    "#print(timeit.timeit(brute_force, number=1))\n",
+    "#print(brute_force())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This did not even terminate. We optimize the sieve by stopping when $p^2 > number$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "74.5315607270004\n",
+      "142913828922\n"
+     ]
+    }
+   ],
+   "source": [
+    "def sieve_of_eratosthenes(number):\n",
+    "    primes = []\n",
+    "    prospects = [n for n in range(2, number)]\n",
+    "    while prospects:\n",
+    "        p = prospects[0]\n",
+    "        prospects = [x for x in prospects if x % p != 0]\n",
+    "        primes.append(p)\n",
+    "        if p * p > number:\n",
+    "            break\n",
+    "    return primes + prospects\n",
+    "\n",
+    "def brute_force():\n",
+    "    return sum(sieve_of_eratosthenes(2000000))\n",
+    "\n",
+    "assert(sieve_of_eratosthenes(10) == [2, 3, 5, 7,])\n",
+    "print(timeit.timeit(brute_force, number=10))\n",
+    "assert(brute_force() == 142913828922)\n",
+    "print(brute_force())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Okay, I honestly did not expect this to be slower than our generator. Gotta keep that in mind for future prime related problems."
    ]
   }
  ],
@@ -29,7 +172,9 @@
    "version": "3.5.4"
   },
   "tags": [
-   "primes"
+   "primes",
+   "brute force",
+   "timeit"
   ]
  },
  "nbformat": 4,