Project Euler Q51 - LO Man Hei

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    "### Q51\n",
    "Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family."
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    "def prime_numbers(n):\n",
    "    result = []\n",
    "    sieve = [True] * (n+1)\n",
    "    for p in range(2, n+1):\n",
    "        if (sieve[p]):\n",
    "            result.append(p)\n",
    "            for i in range(p, n+1, p):\n",
    "                sieve[i] = False\n",
    "    return result \n",
    "\n",
    "def smallest_prime_family(n, search_range=1000000):\n",
    "    prime_list = prime_numbers(search_range)\n",
    "    prime_set = set(prime_list)\n",
    "    for i in prime_list:\n",
    "        s = str(i)\n",
    "        for j in range(3):\n",
    "            temp_set = set(int(s.replace(str(j), str(k))) for k in range(10) if s[0]!= '0' and k!=0)\n",
    "            if len(temp_set&prime_set) == n:\n",
    "                return i\n"
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      "CPU times: user 234 ms, sys: 19.3 ms, total: 254 ms\n",
      "Wall time: 250 ms\n"
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       "121313"
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   "source": [
    "%%time\n",
    "smallest_prime_family(8)"
   ]
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