`bundle exec rails s -b 0.0.0.0 -p 80`

gistfile1.txt

=> Booting Puma
=> Rails 5.0.6 application starting in development on http://0.0.0.0:80
=> Run `rails server -h` for more startup options
** Using session_store: ActionDispatch::Session::MemCacheStore
I, [2017-11-10T15:32:40.722995 #29753]  INFO -- : Initializing websocket worker!
Puma starting in single mode...
* Version 3.7.1 (ruby 2.4.1-p111), codename: Snowy Sagebrush
* Min threads: 5, max threads: 5
* Environment: development
* Listening on tcp://0.0.0.0:80
Exiting
/home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/binder.rb:269:in `initialize': Permission denied - bind(2) for "0.0.0.0" port 80 (Errno::EACCES)
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/binder.rb:269:in `new'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/binder.rb:269:in `add_tcp_listener'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/binder.rb:105:in `block in parse'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/binder.rb:88:in `each'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/binder.rb:88:in `parse'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/runner.rb:144:in `load_and_bind'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/single.rb:87:in `run'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/puma/launcher.rb:171:in `run'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/puma-3.7.1/lib/rack/handler/puma.rb:58:in `run'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/rack-2.0.3/lib/rack/server.rb:297:in `start'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/railties-5.0.6/lib/rails/commands/server.rb:104:in `start'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/railties-5.0.6/lib/rails/commands/commands_tasks.rb:90:in `block in server'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/railties-5.0.6/lib/rails/commands/commands_tasks.rb:85:in `tap'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/railties-5.0.6/lib/rails/commands/commands_tasks.rb:85:in `server'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/railties-5.0.6/lib/rails/commands/commands_tasks.rb:49:in `run_command!'
        from /home/naltun/.rvm/gems/ruby-2.4.1/gems/railties-5.0.6/lib/rails/commands.rb:18:in `<top (required)>'
        from bin/rails:4:in `require'
        from bin/rails:4:in `<main>'

Problem solved: Can't run on an privileged port (ports < 1024). Thanks to coderphive in Freenode #ruby.