My first computer was also a zx81, I still have it too!
it might have run at 3mhz but it only had 1k 
I got mine second hand from my uncle who'd rehoused it in some 3rd party case that had a proper keyboard. It also had a 16K ram pack which fit inside said case where it was _almost_ protected from the "wobble" problem.
When we got a ZX spectrum to replace it, the first thing that struck me was just how much faster it was despite being being all of 250kHz faster. The reason, of course, was that we used to run the zx81 in "slow" mode for the most part. The flickering display when editing was not conducive to productivity.
Of course, when I started learning z80 assembler, I realised just how slow ZX basic was, period.