# https://www.geeksforgeeks.org/sieve-sundaram-print-primes-smaller-n/

from functools import reduce

def sieve_of_sundaram(n):
    # In general Sieve of Sundaram, produces primes smaller
    # than (2*x + 2) for a number given number x.
    # Since we want primes smaller than n, we reduce n to half
    n_new = int((n-2) / 2);
 
    # This array is used to separate numbers of the form i+j+2ij
    # from others where  1 <= i <= j
    marked = [ False ] * (n_new + 1)
 
    # Main logic of Sundaram.  Mark all numbers of the
    # form i + j + 2ij as true where 1 <= i <= j
    for i in range(1, n_new + 1):
        j = i

        while (i + j + 2 * i * j < n_new):
            marked[i + j + 2*i*j] = True
            j += 1
 
    primes = []

    if (n > 2):
        primes.append(2)

    for i in range(1, n_new):
        if (marked[i] == False):
            primes.append(2 * i + 1)

    return primes

primes = sieve_of_sundaram(2000000)

print(reduce(lambda x, y: x + y, primes))

# answer 142913828922