Do you care about the algorithm, or the result? Currently we can factor 11-bit semiprimes fairly reliably, and our hardware is capable of running 16-bit problems. But no, it's not Shor's algorithm. It's conceptually much simpler: implement a multiplication circuit, clamp the output, anneal to find the inputs. Despite not being Shor's algorithm, we've yet to see a competitor demonstrate anything close on the factoring problem.
There's a strange thing in quantum computing happening right now. Certain people believe that there's only one kind of quantum computing, because it's got a provable speedup under yet-unobtainable assumptions. Adiabatic quantum computing, under a similarly unobtainable set of assumptions, can run the same algorithms, polynomially equivalent in time and space. But gate-model gets all the hype.
And speaking of hype, 2017 just called. https://spectrum.ieee.org/computing/hardware/google-plans-to...
They need to choose between removing a large part of the coins from the blockchain or accepting that those coins will be taken by whoever has the technology first. Both options are bad for bitcoin.
I took a very basic course about gate-model quantum computing at my university. The (mathematics) professor would have loved to be able to explain adiabatic quantum computing on a basic level, but was unable to find entry-level material to really understand how it works or what problems it can solve.