#an implementation of the sieve of Eratosthenes
def improved_sieve(n)
  eSieve = (2..n).to_a
  (2..Math.sqrt(n)).each do |i|
    next unless eSieve[i]
    (i*i).step(n, i) { |j| eSieve[j] = nil } #steps by increments of i up to n starting at i*i and sets those elements to nil, marking them for removal
  end
  eSieve.compact
end

puts improved_sieve(2000000).inject(:+)