{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple [Sieve of Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "104743"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import array\n",
    "\n",
    "def primes_upto(N):\n",
    "    S = array.array('B')\n",
    "    S.extend(0 for x in range((N >> 3) + 1))\n",
    "    def set_bit(i):\n",
    "        S[i>>3] |= 1<<(i&7)\n",
    "    def is_bit_set(i):\n",
    "        return S[i>>3]&(1<<(i&7))  \n",
    "    p = 2\n",
    "    for p in range(p, N+1):\n",
    "        if not is_bit_set(p):\n",
    "            yield p\n",
    "            k = 0\n",
    "            while True:\n",
    "                i = p*p + k*p\n",
    "                if i > N:\n",
    "                    break\n",
    "                set_bit(i)\n",
    "                k += 1\n",
    "\n",
    "next(p for i,p in enumerate(primes_upto(1_000_000)) if i+1==10001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "title": "10001st prime"
 },
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