1. A computer-implemented method comprising: receiving, at a computer in a peer-to-peer network, multiple sets of numerical residuals generated in accordance with multiple corresponding prime numbers; determining, based on the prime numbers, whether the sets of numerical residuals are sufficient to recover information encoded by the sets of numerical residuals; recovering the information, when the sets of numerical residuals are sufficient, from at least a portion of the sets of numerical residuals using at least a portion of the prime numbers; wherein the computer comprises a processor and one or more memory devices including a non-transitory tangible medium; wherein the information comprises at least a portion of a media stream, the method comprising: generating sub-streams from the media stream in accordance with corresponding prime numbers; and transmitting the sub-streams to peer devices in the peer-to-peer network.