But how can you prove it but by the letter itself? That's all I'm saying here. That info is verified and protected (SS#) BUT the 4 digits only have 10,000 combination so they are repeated often, but yes, the chance of that going to your house is pretty slim. BUT, if you used it to file fraud watch or something, I do believe it would be inadmissible as evidence. IMO.
And now, the 5th (and unmatching) digit in the picture makes things more interesting. If the 5th digit doesn't match then it isn't your Social Security # and so there isn't a problem.
Yes, it is odd that it went to your address. But without admissible evidence, you have nothing to go on to remedy the situation. I'd tape it shut and write "Opened in Error. Addressee Not Known" and send it back.
That is of course, simply my opinion.