How do I generate the first n prime numbers?

Question

I am learning Ruby and doing some math stuff. One of the things I want to do is generate prime numbers.

I want to generate the first ten prime numbers and the first ten

Answer 1

class Numeric
  def prime?
    return self == 2 if self % 2 == 0

    (3..Math.sqrt(self)).step(2) do |x|
      return false if self % x == 0
    end

    true
  end
end

With this, now 3.prime? returns true, and 6.prime? returns false.

Without going to the efforts to implement the sieve algorithm, time can still be saved quickly by only verifying divisibility until the square root, and skipping the odd numbers. Then, iterate through the numbers, checking for primeness.

Remember: human time > machine time.

Answer 2

Check out Sieve of Eratosthenes. This is not Ruby specific but it is an algorithm to generate prime numbers. The idea behind this algorithm is that you have a list/array of numbers say

2..1000

You grab the first number, 2. Go through the list and eliminate everything that is divisible by 2. You will be left with everything that is not divisible by 2 other than 2 itself (e.g. [2,3,5,7,9,11...999]

Go to the next number, 3. And again, eliminate everything that you can divide by 3. Keep going until you reach the last number and you will get an array of prime numbers. Hope that helps.

http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Answer 3

If you'd like to do it yourself, then something like this could work:

class Integer < Numeric
    def is_prime?
        return false if self <= 1
        2.upto(Math.sqrt(self).to_i) do |x|
            return false if self%x == 0
        end 
        true
    end 

    def next_prime
        n = self+1
        n = n + 1 until n.is_prime?
        n   
    end 
end

Now to get the first 10 primes:

e = Enumerator.new do |y|
    n = 2
    loop do
        y << n
        n = n.next_prime
    end
end

primes = e.take 10