A simple implementation of a core permission check in Drupal 7

core_permissions.php

<?php
/**
 * Implements hook_init().
 *
 * Runs every time a page is requested on the site.
 */
function my_custom_module_init() {
  if (user_access('access content')) {
    drupal_set_message(t('User has Drupal core access content permission'));
  }
  else {
    drupal_set_message(t('User does not have Drupal core access content permission'));
  }
}