Prime in Golden Tree

Shiver in ecstasy, Clifford A. Pickover in his twitter account showed a new kind, amazing prime number :

Which is the prime number of the form $10^{2k} - 10^{k} - 1$, where $k=253$. It will be nice to call “Prime in Golden Tree”, because if such a quadratic form equals 0 then the real solution will explain “original root” that follows golden ratio. As I wrote earlier in this blog, decimal expansion of the form $\displaystyle \frac{1}{10^{2k}-10^{k}-1}$ follows Fibonacci Sequence.

This is amazing prime number. This will invite us to know this kind of prime number better, and the associated quadratic “tree” formula. And in a broader sense, it will invite us on a deeper curiosity about the golden ratio and our universe.

And yes, Shiver in ecstasy.