def sieve_of_eratosthenes(n):
    """
    Calculate the first n prime numbers using the Sieve of Eratosthenes algorithm.
    """
    limit = 10000  # Start with an arbitrary limit
    primes = []
    while len(primes) < n:
        limit *= 2  # Double the limit if not enough primes are found
        is_prime = [True] * (limit + 1)
        p = 2
        while (p * p <= limit):
            if (is_prime[p] == True):
                for i in range(p * p, limit + 1, p):
                    is_prime[i] = False
            p += 1
        primes = [p for p in range(2, limit) if is_prime[p]]
    return primes[:n]

# Calculate the first 1000 prime numbers
first_1000_primes = sieve_of_eratosthenes(1000)
print(first_1000_primes)