#wrong approach, should just do recursive trial division...

def eratosthenes_sieve(n)
  sieve = Array.new(n + 1, true)
  sieve[0] = false
  sieve[1] = false

  2.step(to: Math.sqrt(n)) do |i|
    if sieve[i]
      (i * i).step(to: n, by: i) do |j|
        sieve[j] = false
      end
    end
  end

  result = sieve.map_with_index { |b, i| b ? i : nil }.compact
end

def prime_factors(n)
  nums = eratosthenes_sieve(n).select { |i| n % i == 0 }
  nums = nums + nums.map { |i| n / i }
end

puts eratosthenes_sieve(600851475143)

puts prime_factors(600851475143).max