IMO 1987 - Official problems Question 6

Let $f(x)=x^2+x+p$, $p\in\mathbb N$. Prove that if the numbers $f(0),f(1),\ldots,f([\sqrt{p/3}])$ are primes, then all the numbers $f(0),f(1),\ldots,f(p-2)$ are primes.