007-10001st-prime.ipynb

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    "# 10001st prime\n",
    "## Problem 7 \n",
    "\n",
    "<div class=\"problem_content\" role=\"problem\">\n",
    "<p>By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.</p>\n",
    "<p>What is the 10 001st prime number?</p>\n",
    "</div>"
   ]
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    "from itertools import takewhile, count\n",
    "from math import sqrt\n",
    "\n",
    "def gen_primes():\n",
    "    primes = [2]\n",
    "    yield 2\n",
    "    for n in count(3, step=2):\n",
    "        check_primes = takewhile(lambda p: p <= sqrt(n), primes)\n",
    "        if all(n % p for p in check_primes):\n",
    "            primes.append(n)\n",
    "            yield n"
   ]
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   "source": [
    "from itertools import islice\n",
    "\n",
    "def nth(iterable, n, default=None):\n",
    "    \"Returns the nth item or a default value\"\n",
    "    return next(islice(iterable, n, None), default)"
   ]
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   "source": [
    "def solve(i):\n",
    "    return nth(gen_primes(), i-1)"
   ]
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   "source": [
    "assert solve(6) == 13"
   ]
  },
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   "source": [
    "## Solution"
   ]
  },
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    {
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       "104743"
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     "execution_count": 5,
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   ],
   "source": [
    "solve(10001)"
   ]
  }
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