Is it a prime?

Let $\alpha = 2^{272}$ and $\beta = 545^2$ . We rewrote the original equation to $4\alpha^4+\beta^2$

$4\alpha^4+\beta^2 = (2\alpha^2+\beta)^2-(4\alpha^2\beta) = (2\alpha^2+\beta+2\alpha\sqrt{\beta})(2\alpha^2+\beta-2\alpha\sqrt{\beta})$

As $\sqrt{\beta} = 545$ , then there shall be no radical terms, hence the number above is a product of two other integers and is hence proved to be non-prime.