I wrote some memory test routines a while back - this was for production testing, so I couldn't waste too much time.
The simplest is to write bytes to certain addresses (as MS said), such as 0001, 0002, 0004, etc. E;G; for 15 address lines, you only need to write (then read back) 15 bytes. If you then use a sequence of bytes, whose data follows the same idea (I had a list of 23, so that I was not repeating the same pattern at modulo 16 or something), & then you run the test X (23?) times, starting at a different point in this magic list. After all this, you can be pretty sure that the RAM data & address lines are OK (the chips themselves are very stable these days).

Is this any help?

Regards,

Richard