In [58]:

    

print("Hello World")


    

    




Hello World

In [59]:

    

3**128


    

    
Out[59]:





11790184577738583171520872861412518665678211592275841109096961

In [61]:

    

3**0.5, 3/2


    

    
Out[61]:





(1.7320508075688772, 1.5)

In [27]:

    

def isqrt(n):    
    x, y = n+1, n
    while y < x:
        x, y = y, (y + n // y) // 2
    return x


    

In [19]:

    

print(isqrt(99))


    

    




9

In [30]:

    

def isqrt(n):
    def f(a, b):
        return f(b, (b+n//b)//2) if b < a else a
    return f(n+1, n)


    

In [63]:

    

%%timeit
for i in range(1, 10**5):
    r = isqrt(i)
    assert r**2<=i and (r+1)**2 >= i


    

    




1 loops, best of 3: 450 ms per loop

In [48]:

    

def is_prime(n):
    r = isqrt(n)
    for i in range(2, r+1):
        if n%i == 0:
            return False
    return True


    

In [51]:

    

primes = [n for n in range(2,100) if is_prime(n)]
print(primes)
print(len(primes))


    

    




[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
25

In [56]:

    

def is_prime(n):
    r = isqrt(n)
    return all(n%i !=0 for i in range(2, r+1))


    

In [57]:

    

primes2 = [n for n in range(2,100) if is_prime(n)]
print(primes == primes2)


    

    




True

In [ ]:

    

!git clone https://github.com/tjwei/PythonTutorial