Summation of primes

Problem 10

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.



In [1]:

    
from euler import gen_prime, gen_lt



In [2]:

    
from itertools import islice, takewhile



In [3]:

    
# 20130725 version ported to Python 3
list(zip(gen_prime(), range(6)))[-1][0]









    Out[3]:





13



In [4]:

    
p = list(islice(gen_prime(), 6))
p[-1], p









    Out[4]:





(13, [2, 3, 5, 7, 11, 13])



In [5]:

    
# 20130725 version
list(gen_lt(gen_prime(), 20))









    Out[5]:





[2, 3, 5, 7, 11, 13, 17, 19]



In [6]:

    
list(takewhile(lambda x: x < 20, gen_prime()))









    Out[6]:





[2, 3, 5, 7, 11, 13, 17, 19]



In [7]:

    
def foo(n):
    return sum(gen_lt(gen_prime(), n))



In [8]:

    
n = 10
foo(n)









    Out[8]:





17



In [9]:

    
n = 2000000



In [10]:

    
%timeit foo(n)
foo(n)









    



The slowest run took 169.45 times longer than the fastest. This could mean that an intermediate result is being cached.
1 loop, best of 3: 42.9 ms per loop






    Out[10]:





142913828922



In [11]:

    
def foo(n):
    return sum(takewhile(lambda x: x < n, gen_prime()))



In [12]:

    
%timeit foo(n)
foo(n)









    



10 loops, best of 3: 47.9 ms per loop






    Out[12]:





142913828922