Why do programs always compile to a.out? why not p.out or c.out or g.prog? Historically speaking I know when I run the `cc` command or `gcc` my output generally always compiles to `a.out` unless I have a make file or use a particular flag on the compiler. But why `a.out`? Why not `c.out` or `c.run` or any myriad of a million possibilities?

It is a historical artefact, so in other words a legacy throwback. Historically `a.out` stands for "assembler output".

`a.out` is now only the name of the file but before it was also the file format of the executable.

The `a.out` executable format is nowadays uncommonly supported. The ELF format has wider use, but we still keep the old name for the default output of the C compiler.