Quote:
Originally Posted by Dougy
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?

condition II can be rewritten as
for some i
are you sure you mean that
? if I have
then that's a busted function.
what does bustible mean? Either a function is busted or it is not, bustible sounds like we can do something to the function to make sure it is busted.