can $K, K+l, K+2l,...,K+l^2$ all be primes if $K$ is prime and $l$ $is$ $even$?

Question

Given a $K$ prime number and $l$ $is$ $even$ that satisfy $l<K$.

Is it possible that all the $l+1$ numbers : $K, K+l, K+2l, K+3l,...,K+l^2 $ are primes?

I assume no, but I am struggling to prove it.

***Except from the case $K=3$ and $l=2$

Thanks in advance!