PrimeIt is a small command line program written in ruby that uses an improved version of the sieve of Eratosthenes to generate prime numbers based on the user's input, as well as prime factors

PrimeIt.rb

#PrimeIt is a command line program that uses an improved version of the sieve of Eratosthenes to generate prime numbers based on the user's input.

puts "Welcome to PrimeIt!"

def main_flow(input = nil)
  until input == 0
    puts "Pick any integer greater than 4, and the program will PrimeIt if for you. Press 0 to exit."
    input = Integer(gets.chop) rescue false
    until !!input and (input > 4 or input == 0) do
      puts "Oops! I am afraid #{gets.chop} not an input that can be used by PrimeIt. Let's try again."
      input = Integer(gets.chop) rescue false
    end
    if input == 0
      puts "Thank you for using PrimeIt. Hope to see you again soon!"
    else
      ary = (3..input).step(2).to_a
      primes = [2]
      until ary.length == 0 do
        element = ary.shift
        element_stepper = element**2
        comp =[]
        until ary.last.nil? or element_stepper > ary.last
          comp << element_stepper
          element_stepper += element
        end
        ary = ary - comp
        primes << element
      end

      primes = primes + ary
      if primes.include? input
        puts "Hoorah! #{input} is a prime number."
      else
        puts "Helas! #{input} is just a boring old number."
      end
      puts "There are #{primes.length} prime numbers smaller than or equal to #{input}."
      puts "These are the following:"
      puts primes.join(" ")

      #prime factors
      count_hash = Hash.new(0)
      modulus = input
      until modulus == 1
        primes.each do |prime|
          if modulus % prime == 0
            modulus /= prime
            count_hash[prime] += 1
            break
          end
        end
      end
      factors = ""
      count_hash.each do |key, value|
        factors += "#{key}^#{value}x"
      end
      puts "#{input} can be written in prime factors as #{factors.chop}."

    end
  end
end

main_flow