Slightly more detailed PHP requirements

README.md

@@ -17,7 +17,7 @@ For usage, see [the documentation](https://getcomposer.org/doc/).
 Packages
 --------
 
-Find public dependencies packages on [Packagist](https://packagist.org).
+Find public packages on [Packagist.org](https://packagist.org). For private package hosting take a look at [Private Packagist](https://packagist.com).
 
 Community
 ---------
@@ -34,7 +34,15 @@ By participating in this project and its community you agree to abide by those t
 Requirements
 ------------
 
-PHP 7.2.5 or above.
+#### Latest Composer
+
+PHP 7.2.5 or above for the latest version.
+
+#### Composer 2.2 LTS (Long Term Support)
+
+PHP versions 5.3.2 - 8.1 are still supported via the LTS releases of Composer (2.2.x). If you
+run the installer or the `self-update` command the appropriate Composer version for your PHP
+should be automatically selected.
 
 Authors
 -------