Is it possible to install Nvidia Prime on the 820m GF?

Then your best bet may be the 390 driver hybrid profile with Bumblebee but I have no experience with that, try it and see how it works for you (the prime-run commands would not work with Bumblebee).

sudo mhwd -i pci video-hybrid-intel-nvidia-390xx-bumblebee
reboot
glxinfo | grep 'renderer string'
optirun glxinfo | grep 'renderer string'
primusrun glxinfo | grep 'renderer string'