This is because Ubuntu 13.04 has been end-of-lifed (Mint 15 was released 2013-05-29).
If you absolutely must keep Mint 15, you will need to update
/etc/apt/sources.list.d/official-package-repositories.list to point to the Ubuntu Archive URLs:
deb http://packages.linuxmint.com olivia main upstream import #id:linuxmint_main
deb http://old-releases.ubuntu.com/ubuntu/ raring main restricted universe multiverse
deb http://old-releases.ubuntu.com/ubuntu/ raring-updates main restricted universe multiverse
deb http://old-releases.ubuntu.com/ubuntu/ raring-security main restricted universe multiverse
deb http://archive.canonical.com/ubuntu/ raring partner
The above also means that you will not recieve secrutiy updates or bug fixes for installed software, so you should update to the latest version.
The latest version of Linux Mint is Mint 17, which is based on Ubuntu 14.04 (Trusty Tahr). This is an LTS (Long Term Support) release, and will be supported until April 2019.