Show that the expression does not only generate prime numbers n^2-n+11
Let's assume that the expression only generates prime numbers of the form n^2-n+11. We want to show that this assumption leads to a contradiction.
First, we note that the expression n^2-n+11 is always odd. This is because n^2 and n have the same parity (i.e. they are both even or both odd), and so their difference will always be odd. Adding 11 to an odd number will also give an odd number.
Next, we consider the value of the expression when n=11. Plugging this into the expression gives:
11^2 - 11 + 11 = 121
We can see that 121 is not a prime number, which contradicts our assumption that the expression only generates prime numbers of the form n^2-n+11.
Therefore, we have shown that the expression does not only generate prime numbers of the form n^2-n+11.