In [13]:

    

def primes_beneath(N):
    primes_found = [2]
    i = 2
    while primes_found[-1] < N:
        i += 1
        d = 1
        sqrt_i = sqrt(i)
        for p in primes_found:
            if i % p == 0:
                d = i / p
                break
            if p > sqrt_i:
                break
        if d == 1:
            primes_found.append(i)
        i += 1 # can skip evens.
    return primes_found[:-1]

pr = primes_beneath(10)
print pr, sum(pr)


    

    




[2, 3, 5, 7] 17

In [14]:

    

pr = primes_beneath(2e6)
print sum(pr)


    

    




142913828922

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