Amd 386dx-40

Going trough my old hardware I found my DX-40. Its case was part of my spare hardware shelves (two cases, a board, yet two cases again, another board, etc., you got it). The shelves also contained some venerable Pentium 60s, more worth for the gold than the performance.
I will try to fire-up ye olde DX40, so it can be used to determine which of the umphteen 32-pin memory sticks are 1 Mb and which 4Mb. After I established that it is just a matter of waiting till time-travel becomes possible. I once blew my complete holiday bonus on a mere 2Mb of 32-pin memory, it was freaking expensive. So I have a potential fortune in my hands!
Doubling my memory on my AMDSX-25 from 2 to 4 Mb did wonders. The system ended up with 8x4=32 Mb and an IIT copro, before I switched to my next great AMD chip: the K6III-400, which I just discovered on the attic. Might give it a try at the next simap challenge....

See if it will run any of the non-CPU intensive projects like Freehal BOINC or Dimes non-BOINC. Maybe try it on BOINC Mersenneprime as you can select "small" tasks there.

What OS can you use on that machine? I'm thinking only DOS and similar command line OSes, and maybe some very lightweight linux distro.

The 386 was able to run Win95.
It was also the first to be able to address 4GB RAM - not that any one of us could afford that much RAM back then to test that feature
My last 386 was a DX-40 too and it ran the PC-Tools, Central Point and Norton desktops at various times.
I think I ran my first linux distro on my 486-DX though, but I am sure that others did run linux on a 386.
You'd have to go back a bit to find the right kernels though.
The latest modern distros have been ditching support for the old chipsets and archs acknowledging that the old distro versions are still available somewhere.
There's about 6 variations of DOS that will running on there like 4DOS,
although I think MSDOS 6.1.x probably won't and I can't remember why. Just an engram hanging around in my lobes.
You'll need to configure EMM386 to use the expanded memory and then RAMspeed (or similar) to cache the extended ram.

Oh memory lane >!!<

The AMD 386DX-40 could run OS/2 Warp3 as well (Heck, a 386SX-20 could even run OS/2 2.x), and I think Windows NT4 might even work on it.
Most 386 motherboards would not support more than 32 Mb memory, but in those days that was more than most people were able to buy anyway.
I have a harddisk around here with 4 different DOS versions on it, MS-DOS, PC-DOS, FreeDOS and DR-DOS, used to test which would give the most memory under 640k -with or without QEMM, to use the extended and expanded memory even better than EMM386-. FreeDOS won: 639k free!
The AMD386DX-40 was the first AMD CPU that people actively to have in their mobo's, in my recollection. This was because it was the fastest (not clocked doubled or tripled) running 80386 chip around, by virtue of its 32-bit 40 MHz internal bus.
How time files. Nowadays you can't use it to run a modern major OS, because they all went 64-bit but in those days it ran all OS-es that were meant for x86. 8-bit (e.g. CP/M), 16-bit (DOS), 32-bit (Windows 2 or 3.x): it did. You can still run FreeDOS on it, if you have a 386DX-40 board -like me- and want both legacy and up-to-date 16-bit software to run a a system.
If you are looking for L1 cache: look on the motherboard itself. If you are looking for a FPU-unit: stick in a 387DX-40 and make sure it a Cyrix FasMath Cyrix 387DX-40/Cyrix 387DX+, which has its own 8k L1 cache. They are rumoured to be the best 80387 chips.
The 386DX-40 was able to do 9 MIPS (Milions of Instructions Per Second) and had a IPC (Instructions Per Cycle) of 0.225, but because values like MIPS, MFLOPS, and IPC all varried from one program to another, one of the most commonly used measures of performance became the processor frequency, which eventually lead to the "Pentium 4 Hothead" -by then standards- with Intel.