Project Euler Q46 - LO Man Hei

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    "### Q46\n",
    "What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?"
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    "def prime_numbers(n, max_len = False):\n",
    "    result = []\n",
    "    if max_len:\n",
    "        n = max_len**2//5000 + max_len*20\n",
    "    sieve = [True] * (n+1)\n",
    "    for p in range(2, n+1):\n",
    "        if (sieve[p]):\n",
    "            result.append(p)\n",
    "            if max_len and len(result) >= max_len:\n",
    "                return result\n",
    "            for i in range(p, n+1, p):\n",
    "                sieve[i] = False\n",
    "    return result\n",
    "\n",
    "def goldbach_conjecture(search_range = 10000):\n",
    "    prime_set = set(prime_numbers(search_range))\n",
    "    odd_composite_set = set(range(3,search_range+1,2)).difference(prime_set)\n",
    "    for i in sorted(list(odd_composite_set)):\n",
    "        j = 1\n",
    "        is_match = False\n",
    "        while 2*j*j < i:\n",
    "            if (i - 2*j*j) in prime_set:\n",
    "                is_match = True\n",
    "                break\n",
    "            j += 1\n",
    "        if not is_match:\n",
    "            return i"
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      "CPU times: user 1.38 ms, sys: 475 µs, total: 1.85 ms\n",
      "Wall time: 1.85 ms\n"
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    "%%time\n",
    "goldbach_conjecture()"
   ]
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