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   "source": [
    "# Euler Problem 7\n",
    "\n",
    "By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.\n",
    "\n",
    "What is the 10 001st prime number?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reuse our prime functions and use a trick from [stackoverflow](https://stackoverflow.com/questions/2300756/get-the-nth-item-of-a-generator-in-python) to get the nth element."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "104743\n"
     ]
    }
   ],
   "source": [
    "import itertools\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 get_nth_prime(n):\n",
    "    ps = prime_generator_function()\n",
    "    return next(itertools.islice(ps, n - 1, n))\n",
    "\n",
    "assert(get_nth_prime(6) == 13)\n",
    "print(get_nth_prime(10001))"
   ]
  }
 ],
 "metadata": {
  "completion_date": "Wed, 20 Aug 2014, 15:40",
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  "tags": [
   "prime",
   "nth prime",
   "nth",
   "generator"
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