//
// program to compute primes <= n using sieve of Eratosthenes
//
import scala.io.StdIn._

println("largest number to try?")
val n = readInt

//
// isPrime(i) will be true if i is prime, false otherwise
//
val isPrime = Array.fill(n+1)(true)

isPrime(0) = false
isPrime(1) = false

// initially i ranged from 2 to n, but we can do better:
// any non-prime will have at least one prime factor <= sqrt(n)
for (i <- 2 to math.ceil(math.sqrt(n)).toInt) {
  if (isPrime(i)) {
    // "cross out" multiples of i
    println("crossing out multiples of "+i)
    for (j <- i*2 to n by i) {
      if (isPrime(j)) println("crossing out "+j)
      isPrime(j) = false
    }
  }
}

println()
println("primes:")
for (i <- 0 to n) {
  if (isPrime(i)) println(i)
}