def gcd(x, y):
    if 0 == y:
        return x
    else:
        return gcd(y, x % y)


def lcm(x, y):
    return x * y // gcd(x, y)


def pow_mod(base, exp, mod):
    result = 1
    for digit in bin(exp)[2:]:
        result = result ** 2 % mod
        if '1' == digit:
            result = result * base % mod
    return result


def make_prime(limit):
    if limit < 2: return
    yield 2
    if limit < 3: return
    yield 3
    if limit < 5: return

    n = (limit + 1) // 6

    a = [True] * n
    b = [True] * n

    for i in range((int(limit ** 0.5) + 1) // 6 + 1):
        if a[i]:
            p = 6 * i + 7
            f = 7 * i + 7
            g = 5 * i + 5
            a[f::p] = [False] * ((n - f - 1) // p + 1)
            b[g::p] = [False] * ((n - g - 1) // p + 1)
        if b[i]:
            p = 6 * i + 5
            f = 5 * i + 3
            g = 7 * i + 5
            a[f::p] = [False] * ((n - f - 1) // p + 1)
            b[g::p] = [False] * ((n - g - 1) // p + 1)

    for i in range(n):
        if b[i]:
            yield 6 * i + 5
        if a[i]:
            yield 6 * i + 7