from math import sqrt
def  sieve_of_eratosthenes(primes, from_n, to_n):
    length = to_n - from_n
    arr = [True]*length + [False]
    for p in primes:
        for i in range((to_n - 1 - (from_n-1)//p*p)//p):
            b = -from_n % p
            arr[b + p*i] = False
    for i in range(int(sqrt(to_n)) + 1 - from_n):
        if arr[i]:
            p = from_n + i
            for j in range(1, (to_n - 1 - (from_n-1)//p*p)//p):
                b = -from_n % p
                arr[b + p*j] = False
    for i in range(to_n - from_n + 1):
        if arr[i]:
            primes.append(from_n + i)
    return primes

class Primes:
    def stream():
        counter1 = 0
        counter2 = 1
        primes = sieve_of_eratosthenes([2], 3, 100000)
        length = len(primes)
        while True:
            print(primes[counter1])
            yield primes[counter1]
            if counter1 + 1 == length:
                primes = sieve_of_eratosthenes(primes, counter2*100000, (counter2+1)*100000) # 100000 - размер сегмента решета
                length = len(primes)
                counter2 += 1
                if counter2 == 4:                                                            # 4 - количество сегментов
                    n = primes[-1] + 2
                    break
            counter1 += 1
            """
        while True:
            is_primal = True
            for p in primes:
                if p > sqrt(n):
                    break
                if n % p == 0:
                    is_primal == False
            if is_primal:
                print(n)
                yield n
            n += 2
            """