**Definition**: Let

be a function. Then if, for all

, one of the following is true:

(i)

is not prime for some

. (where

and

, i.e. function composition)

(ii)

for distinct

.

then

is called a

*busted* function.

Some functions are easily busted. E.g.

for some

, or

. While some functions are not bustible. E.g. Any function satisfying

, where

is the

prime.

**Question**: What functions are busted?

The motivation behind this conjecture is to disprove anyone who claims something like "if

is a prime, and

, then

is a sequence of primes". A function becomes 'busted' when it stops producing new primes.

Has this been done before? Can anyone easily bust some functions?