Well, memtest errors typically should mean your ram is faulty, and by the looks of it quite a lot of this.
With a problem like this I'd
replace the ram (and if you have another laptop of a similar vintage, check with known good ram!)
If that doesn't help, something else may be broken (like your memory controller). Considering sandy and ivy bridge have the memory controller in the CPU, if replacing the ram dosen't help, I'd probably think you would end up replacing the laptop.
As an aside, it seems some flavours of linux actually have a patch that lets you blacklist bad ram. I've never used it before but its worth a look if you do end up finding its bad ram, and experiment with it. I'd hardly consider it production grade but its worth messing with. I'd refer you to U&L for more details