When is $f(y)$ prime? Find all prime numbers that can be expressed as :
 $f(y)=y^{2015}+y+1$, where $y$ is a natural number. $y=1$ gives us 3, but how do we find others or prove that there can be no other??

Hint
Use the fact that 
$$x^{2015}+x+1 = x^{2015}-x^2+(x^2+x+1)=x^2(x^{3\times 671}-1)+(x^2+x+1) = x^2(x^{3}-1)(x^{3\times 670}+x^{3\times 669}+\dots+x^3+1)+(x^2+x+1) = (x^2+x+1)(x^2(x-1)A+1)$$
where $A = x^{3\times 670}+x^{3\times 669}+\dots+x^3+1$
