class Prime::EratosthenesSieve

# File lib/prime.rb, line 423
def initialize
  @primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101]
  # @max_checked must be an even number
  @max_checked = @primes.last + 1
end

# File lib/prime.rb, line 429
def get_nth_prime(n)
  compute_primes while @primes.size <= n
  @primes[n]
end

# File lib/prime.rb, line 435
def compute_primes
  # max_segment_size must be an even number
  max_segment_size = 1e6.to_i
  max_cached_prime = @primes.last
  # do not double count primes if #compute_primes is interrupted
  # by Timeout.timeout
  @max_checked = max_cached_prime + 1 if max_cached_prime > @max_checked

  segment_min = @max_checked
  segment_max = [segment_min + max_segment_size, max_cached_prime * 2].min
  root = Integer(Math.sqrt(segment_max).floor)

  sieving_primes = @primes[1 .. -1].take_while { |prime| prime <= root }
  offsets = Array.new(sieving_primes.size) do |i|
    (-(segment_min + 1 + sieving_primes[i]) / 2) % sieving_primes[i]
  end

  segment = ((segment_min + 1) .. segment_max).step(2).to_a
  sieving_primes.each_with_index do |prime, index|
    composite_index = offsets[index]
    while composite_index < segment.size do
      segment[composite_index] = nil
      composite_index += prime
    end
  end

  segment.each do |prime|
    @primes.push prime unless prime.nil?
  end
  @max_checked = segment_max
end