Elliptic Curve Primality Proving (ECPP) is a mathematical method used to determine whether a number is prime. It leverages the properties of elliptic curves, which are special types of curves defined by cubic equations. By analyzing these curves and their points, ECPP can efficiently verify the primality of large numbers, making it useful in fields like cryptography. The process involves constructing an elliptic curve and performing calculations related to its points. If certain conditions are met, the number is confirmed as prime. ECPP is known for its speed and effectiveness, especially for very large integers, compared to traditional primality tests.