Is a pattern proof? Let's say I want a formula that takes any number and makes it into 170, and I come up with a formula that I think does it. If I plug 1 into it, 2 into it, 3 into it, etc. up to a pretty large number and it works, can I call the formula proven? 

No you can't... A classical example of such mistake:

3,5,7 are prime numbers and so every odd number is prime

See also this question for much more counter-examples.
