In a letter written to Landau in 1935, Schur stated that for any integer $t>2$, there are primes $p_1<p_2<\cdots <p_t$ such that $p_1+p_2>p_t$. In this note, we use the Prime Number Theorem and extend Schur’s result to show that for any integers $t\ge k\ge 1$ and real $ϵ>0$, there exist primes $p_1<p_2<\cdots <p_t$ such that $$p_1+p_2+\cdots +p_k>(k-ϵ)p_t.$$