def sieve_primes(n):
    if n < 2:
        return []
    prime = [True] * (n + 1)
    prime[0] = prime[1] = False
    p = 2
    while p * p <= n:
        if prime[p]:
            for multiple in range(p * p, n + 1, p):
                prime[multiple] = False
        p += 1
    return [value for value in range(2, n + 1) if prime[value]]