> None at this time, but until the advent of modern cryptography, the same was true of primality. I'm not sure that this is true, at least if you are flexible

> None at this time, but until the advent of modern cryptography, the same was true of primality. I'm not sure that this is true, at least if you are flexible about what counts as an ‘application’. The concept of divisibility, and then of primality, surely developed from considerations of how a certain number of objects could, or could not, be broken into groups, say for storage or transport. To know that there are several ways to group 24 objects, but only two (trivial) ways to group 23 objects, is an application, even if it's not especially sophisticated.