I don't think child prodigies as commonly known exist in computer programming. A child can learn concertos or even write concertos, but not the comparable version of a concerto in code.
I have two existence proofs in mind that this isn't true.
One of them runs a very large venture backed company and is active right here on this site, the other you've likely never heard of, is super modest and absolutely blew me away with their ability while still in high school, by which time they'd been programming for more than a decade. Some kids really are amazingly capable.
I wasn’t a child prodigy but I wrote a word processor (on a Wang PCS II) that was used for years later by (high) school administration when I was in the tenth grade. By the 11th grade my first after school job was writing commercial software.
One of them runs a very large venture backed company and is active right here on this site, the other you've likely never heard of, is super modest and absolutely blew me away with their ability while still in high school, by which time they'd been programming for more than a decade. Some kids really are amazingly capable.