20060222, 08:01  #1 
Aug 2004
Melbourne, Australia
2^{3}·19 Posts 
Busted functions
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? Last fiddled with by Dougy on 20060222 at 08:03 
20060222, 09:23  #2  
Cranksta Rap Ayatollah
Jul 2003
1010000001_{2} Posts 
Quote:
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. 

20060222, 12:09  #3  
Aug 2004
Melbourne, Australia
152_{10} Posts 
Thanks for your response.
Quote:
Quote:
Your example is a busted function, however a rather trivial one. It would perhaps be possible to define , but then is not well defined. Basically the functions of any real interest are smooth functions, like polynomials, exponentations, etc.. Quote:
Definition: Let be a function. Then if there exists a proof that is busted, we say is bustible. Last fiddled with by Dougy on 20060222 at 12:15 

20060222, 12:50  #4  
Aug 2004
Melbourne, Australia
2^{3}·19 Posts 
Quote:
It is possible to create a related function such that whenever , and whenever is not a natural number. But then this would be asking a different question. Last fiddled with by Dougy on 20060222 at 12:52 

20060222, 20:59  #5 
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Oops. I think mine implies yours, but not the converse

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