update readme

README.md

@@ -1,8 +1,6 @@
 # Prime
 
-Welcome to your new gem! In this directory, you'll find the files you need to be able to package up your Ruby library into a gem. Put your Ruby code in the file `lib/prime`. To experiment with that code, run `bin/console` for an interactive prompt.
-
-TODO: Delete this and the text above, and describe your gem
+Prime numbers and factorization library.
 
 ## Installation
 
@@ -22,13 +20,22 @@ Or install it yourself as:
 
 ## Usage
 
-TODO: Write usage instructions here
+```ruby
+require 'prime'
 
-## Development
+# Prime is the set of all prime numbers, and it is Enumerable.
+Prime.take(4)             #=> [2, 3, 5, 7]
+Prime.first(4)            #=> [2, 3, 5, 7]
+Prime.each(7).to_a        #=> [2, 3, 5, 7]
 
-After checking out the repo, run `bin/setup` to install dependencies. Then, run `rake test` to run the tests. You can also run `bin/console` for an interactive prompt that will allow you to experiment.
+# Determining whether an arbitrary integer is a prime number
+Prime.prime?(7)           #=> true
+8.prime?                  #=> false
 
-To install this gem onto your local machine, run `bundle exec rake install`. To release a new version, update the version number in `version.rb`, and then run `bundle exec rake release`, which will create a git tag for the version, push git commits and tags, and push the `.gem` file to [rubygems.org](https://rubygems.org).
+# Factorization in prime numbers
+Prime.prime_division(779)                           #=> [[19, 1], [41, 1]]
+Prime.int_from_prime_division([[19, 1], [41, 1]])   #=> 779
+```
 
 ## Contributing