```json
{
  "documents": [
    {
      "data": "def sieve_of_eratosthenes(limit):\n    \"\"\"\n    Generate all prime numbers up to the given limit using the Sieve of Eratosthenes algorithm.\n    \"\"\"\n    is_prime = [True] * (limit + 1)\n    p = 2\n    while (p * p <= limit):\n        if (is_prime[p] == True):\n            for i in range(p * p, limit + 1, p):\n                is_prime[i] = False\n        p += 1\n    prime_numbers = [p for p in range(2, limit + 1) if is_prime[p]]\n    return prime_numbers\n\n\ndef first_n_primes(n):\n    \"\"\"\n    Calculate the first n prime numbers using the Sieve of Eratosthenes algorithm.\n    \"\"\"\n    # Estimate an upper limit for the nth prime number using the approximation n * log(n * log(n))\n    # This is a rough estimate and ensures we have a high enough limit to find the first n primes.\n    import math\n    if n < 6:\n        limit = 15\n    else:\n        limit = int(n * math.log(n * math.log(n)))\n    primes = sieve_of_eratosthenes(limit)\n    return primes[:n]\n\n# Example usage:\nfirst_1000_primes = first_n_primes(1000)\nprint(first_1000_primes)\n",
      "mimeType": "text/plain",
      "comment": "This function calculates the first 1000 prime numbers using the Sieve of Eratosthenes algorithm."
    }
  ],
  "continue": false
}
```