Why not compress this AGAIN

If your compression algorithm is any good, it should *not* be able to compress the output a second time. Compressing before encryption is vital--it makes brute force and plaintext attacks much more difficult. On compression forever: I read a science fiction short story once where (not sure of title or author, but it is a classic) a bunch of geniuses are ostensibly sent to another planet to "explore", but the people sending them had a different motive: get them away from Earth and give them time to dream up cool stuff. Okay, so they dream up way cool stuff, but have this problem with transmission bandwidth back to Earth. Then they figure out that any message can be encoded in prime numbers like: 2^a * 3^b * 5^c * 7^d... where a b c d are the character values (ascii or letter A==0, B==1, etc.). After a message is encoded, the result is a *big number*. This number is not more compact than the original message, but the clever geniuses flying to Tau Ceti (or wherever) figured out how to factor the number down to things like M^N + P^Q, where the number of bits needed to write down the factorization was very small, say, 100 bits or so. THEN, they ship this factorization back to Earth and save bandwidth and it encodes the whole Encyclopedia Gallactica. This scheme doesn't work because factoring is much harder than using other compression techniques. Paul E. Baclace peb@procase.com