def sieve_of_eratosthenes(limit):
    primes = []
    is_prime = [True] * (limit + 1)
    for num in range(2, limit + 1):
        if is_prime[num]:
            primes.append(num)
            for multiple in range(num * num, limit + 1, num):
                is_prime[multiple] = False
    return primes


def is_prime_trial_division(n):
    if n <= 1:
        return False
    if n <= 3:
        return True
    if n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i * i <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True


# Calculate the first 1000 prime numbers
limit = 7920  # A rough estimate to ensure we get at least 1000 primes
primes = sieve_of_eratosthenes(limit)
first_1000_primes = primes[:1000]

# Validate the list of primes
validated_primes = [p for p in first_1000_primes if is_prime_trial_division(p)]

# Check if the validation was successful
assert len(validated_primes) == 1000, "Validation failed: Not all numbers are prime"

print("First 1000 primes calculated and validated successfully.")