#10 - Summation of primes

26 Jul 2015 in Project Euler on 5%

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

Find the sum of all primes below two million.

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Since finding primes is the main crux of the problem, I will refran from using the primesieve package. In this case, I will use the same sieve we generated from #7 - 10001st prime. This time we need to go until two million. To get the actual values, we will just use enumerate, which pairs the index with the actual value.

# file: "problem010.py"
limit = 2000000
sieve = [True] * (limit + 1)
sieve[0] = False
sieve[1] = False
# Start at index 2, so the index = prime number
p = 2
while p < limit + 1:
    # If it's composite, then go to the next one
    if not sieve[p]:
        p += 1
        continue
    # Mark all multiples
    for i in range(2 * p, limit + 1, p):
        sieve[i] = False
    p += 1

s = 0
for i, mark in enumerate(sieve):
    if mark:
        s += i
print(s)

Running the loop,

142913828922
1.7028809000039473 seconds.

Therefore, the sum of all primes under two million is 142913828922.