How can i calculate prime of Elliptic Curve? In many articles i have found directly the calculation of prime elliptic curve. How can i calculate this prime $p$ ? For example if I consider NIST P-256, $ p = 2^{256}-2^{224}+2^{192}+2^{96}-1$. Why ? Is there a formula ? Thanks for your support.
This prime $p$ corresponds to the size on the base field $\mathbb F_p$ on which is defined the elliptic curve. It has not been computed, it has been chosen. It is chosen to satisfy a few properties, like, of course, being prime, but also being large enough (here, 256 bits), and allowing fast computations modulo $p$.
Maybe when you say "prime elliptic curve", you mean elliptic curves with a prime number of points? The number of points is not the prime $p$, and is computed using the Schoof-Elkies-Atkin algorithm.