The Pell-Fermat equation

It is well known that the Pell-Fermat equation $x^2-n\times y^2=1$ (1) has always solutions when n is not square.
But for the symetrical equation $x^2-n\times y^2=-1$ (2), solutions are much rare.

For instance, if $n\le 100$, this equation has solutions for only 20 values.

For how many $n\le 5000000$, has the equation (2) solutions?

[My timing: 70 sec]