In case you try to download the latest 1.x version nowadays, to get the latest version you can go to https://magento.com/tech-resources/download click on 'Release Archive' and look for 'Downloader - 1.x' (waay down, bottom half of the page).
DON'T do what i did and go looking for a specific 1.x version number like 18.104.22.168 or sth. because you WON'T find that on the official page.
There is a downloader that will automagically download the latest 1.x version for you, thats what you have to get, the DOWNLOADER.
If you want a SPECIFIC 1.x version, go to https://github.com/OpenMage/magento-mirror, as the name says they are a mirror for the Magento 1.x releases.
You can't download specific 1.x versions from the Magento.com page anymore, for the latest version get the 'Downloader 1.x' from the oficial page here, or go to OpenMage which is an unoficial mirror for all 1.x releases.
As the development of Magento 1 has stopped (in June 2020) there will be no more updates for it from Adobe.
The good new is that there is a great fork by OpenMage though which is being developed by the community. It is called Magento LTS.
It is completely backwards compatible to the latest Magento 1 version.