```json
{
  "documents": [
    {
      "data": "def sieve_of_eratosthenes(limit):\n    primes = []\n    is_prime = [True] * (limit + 1)\n    for num in range(2, limit + 1):\n        if is_prime[num]:\n            primes.append(num)\n            for multiple in range(num * num, limit + 1, num):\n                is_prime[multiple] = False\n    return primes\n\n\ndef is_prime_trial_division(n):\n    if n <= 1:\n        return False\n    if n <= 3:\n        return True\n    if n % 2 == 0 or n % 3 == 0:\n        return False\n    i = 5\n    while i * i <= n:\n        if n % i == 0 or n % (i + 2) == 0:\n            return False\n        i += 6\n    return True\n\n\n# Calculate the first 1000 prime numbers\nlimit = 7920  # A rough estimate to ensure we get at least 1000 primes\nprimes = sieve_of_eratosthenes(limit)\nfirst_1000_primes = primes[:1000]\n\n# Validate the list of primes\nvalidated_primes = [p for p in first_1000_primes if is_prime_trial_division(p)]\n\n# Check if the validation was successful\nassert len(validated_primes) == 1000, \"Validation failed: Not all numbers are prime\"\n\nprint(\"First 1000 primes calculated and validated successfully.\")",
      "mimeType": "text/plain",
      "comment": "This script calculates the first 1000 prime numbers using the Sieve of Eratosthenes and validates them using trial division."
    }
  ],
  "continue": false
}
```