In this case, nothing that I know of. Again, that's the kind of math that is classified as "number theory". It's just pure investigation of relationships between numbers. Occasionally you gain some insight that is useful.
A lot of cryptography used to be just number theory until computers came along and were powerful enough to make use of it. How to tell if something if someting is divisible by 3. Checksums as used on credit cards. Euler's algorighm.
No, sexy primes don't really have a point other than they are identified and there is probably some unused conjecture that they are infinite in number.