def sieve_of_eratosthenes(n):
    """
    Generate a list of prime numbers up to n using the Sieve of Eratosthenes algorithm.
    """
    is_prime = [True] * (n + 1)
    p = 2
    while (p * p <= n):
        if (is_prime[p] == True):
            for i in range(p * p, n + 1, p):
                is_prime[i] = False
        p += 1
    prime_numbers = [p for p in range(2, n) if is_prime[p]]
    return prime_numbers

# We need to find the upper limit for the sieve to ensure we get at least 1000 primes.
# A rough estimate for the nth prime is n * log(n * log(n)), but we'll use a safe upper bound.

def find_first_1000_primes():
    upper_limit = 10000  # A safe upper limit to ensure we get at least 1000 primes
    primes = sieve_of_eratosthenes(upper_limit)
    return primes[:1000]

# Get the first 1000 prime numbers
first_1000_primes = find_first_1000_primes()

# Print the first 1000 prime numbers
print(first_1000_primes)