Some groups have even been running Shor's algorithm on multi-qubit computers. https://en.wikipedia.org/wiki/Quantum_computer#Developments It requires the qubits to be entangled to do the computation, and in the later ones (not IBM's 2001 work) the researchers did observe entanglement.
Technically, you can run Shor's algorithm on non quantum computers, with an exponential speed up (but fully within capabilities of modern computing vs. small quantities of qubits)