Edigles Guedes, Raja Rama Gandhi, Exploring Prime Numbers and Modular Functions II: On the Prime Number via Elliptic Integral Function, BMSA Volume 7, Bulletin of Mathematical Sciences and Applications (Volume 7) https://www.scipress.com/BMSA.7.32 Abstract: The main goal this paper is to develop an asymptotic formula for the prime number, using elliptic integral function. Keywords: