**Does the equation in positive integers $\,(n,\,y)$
$$\prod_{k=1}^n(p_k^2-1)=y^2$$
only have the solution $(3,\,24)\,$?**

I asked a more general question here.

The computational complexity of the problem can be slightly reduced considering that $$(2^2-1)(3^2-1)(5^2-1)=24^2$$ $$24|p^2-1\;\;\;\;\;p\gt3$$ Therefore, one can consider the equivalent problem $$\frac{\prod_{k=1}^{2n+3}(p_k^2-1)}{24^{2(n+1)}}=z^2$$ and the known solution $\,(n,\,z)=(0,\,1)$.

**Up to $\,n=5\cdot10^4-2\,$ I have not found any other solution.**

Many thanks.