Can there be a prime of the form $2y^2s + ys - 4y^2 +1$

Question

Can there be a prime of the form

$2y^2s + ys - 4y^2 +1$

where $y$ and $s$ are positive integers

Forgot to say, $s \ge 3$ and $y \ge 1$

Answer 1

Hint: $$\begin{aligned}2y^2s+ys-4y^2+1&=ys(2y+1)-(2y-1)(2y+1)\\ &=(ys-2y+1)(2y+1) \end{aligned}$$ and $2y+1>1$.