# エラトステネスの篩
def eratos(n):
    primes = [True] * (n+1)
    primes[0], primes[1] = False, False
    for i in range(2, int(n**0.5)+1):
        if primes[i]:
            for j in range(i**2, n+1, i):
                primes[j] = False
    ret = [num for num, is_prime in enumerate(primes) if is_prime]
    return ret