Can You Run Linux On An Intel 4004 CPU From 1971? Surprisingly, Yes!
That's why unhinged hardware-and-software hacking lunatic (which we say in the fondest way possible) Dmitry Grinberg had to use an emulator to get Linux to boot on an Intel 4004 microprocessor from 1971, a full twenty years before Linux itself came into existence. This was the world's first fully-integrated microprocessor, and it was originally designed to allow for more compact electronic calculators. Grinberg says that the chip's roots really show through in its feature set, which has almost none of the functions you would expect from any newer CPU.
It is technically a CPU, though, so by creating a custom baseboard with a specialized clock generator, 16MB of RAM, and no other processors onboard, Grinberg has indeed managed to boot Linux on an Intel 4004—by emulating a Digital DECstation 2100. That machine had a 32-bit MIPS R3000 processor running at 8 MHz; the Intel 4004 works in 4-bit nibbles and runs at 790 KHz. Yes, that's 0.79 MHz.
This is about as fast as you'd expect. Well, we sort of gave it away in the headline, but yeah—booting Linux on the emulated DECstation takes nearly five entire days, and Grinberg isn't booting into a graphical environment; doing so would take months. This is the most basic Debian configuration possible, booting directly into a bash shell.
It is a functional system; Grinberg demonstrates this by running a few commands including an 'ls' directory listing that takes an entire day to list just a few files and directories on a single line. He also runs a simplistic Mandelbrot fractal calculator that displays the results in ASCII art form on the command line; this takes more than a day in itself.