Sieve of Eratosthenes in Ruby

Question

Rather than scraping a Ruby version of this algorithm off the net I wanted to create my own based on its description here. However I cannot figure out two things

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Answer 1

There's a faster implementation at www.scriptol.org:

def sieve_upto(top)
  sieve = []
  for i in 2 .. top
    sieve[i] = i
  end
  for i in 2 .. Math.sqrt(top)
    next unless sieve[i]
    (i*i).step(top, i) do |j|
      sieve[j] = nil
    end
  end
  sieve.compact
end

I think it can be improved on slightly thus:

def better_sieve_upto(n)
  s = (0..n).to_a
  s[0] = s[1] = nil
  s.each do |p|
    next unless p
    break if p * p > n
    (p*p).step(n, p) { |m| s[m] = nil }
  end
  s.compact
end

...largely because of the faster array initialisation, I think, but it's marginal. (I added #compact to both to eliminate the unwanted nils)