We have created the architecture of a quantum multicomputer and analyzed its performance for running Shor's algorithm for factoring large numbers. In this paper, we combine fault tolerance techniques with performance goals for our architecture, which uses a linear interconnect and six logical qubits per node. Our performance target of factoring a 1,024-bit number in one month requires teleporting 6.2 logical qubits per second on each link in the system, which translates to 3,300 physical teleportations per second on each link. Starting from a Bell state with fidelity F∈=∈0.638, as a qubus-based cavity QED interconnect might generate with a qubit-to-qubit loss of 3.4dB, about 1.5 million physical entanglement attempts per second are enough to reach this level of performance. Our analysis suggests that systems capable of solving classically intractable problems are well within reach; once basic technological hurdles are overcome, the multicomputer architecture supports rapid scaling to very large systems.