The Sieve of Eratosthenes and the π(n) function: A pedagogical proposal.

A pedagogical proposal for the study of prime numbers, overcoming the didactic stagnation that has surrounded the Sieve of Eratosthenes for over two millennia. Through the implementation of an approach based on algorithmic thinking and the current e-learning ecosystem, an optimization of the sieve is introduced using index bijection and the application of the 'Wheel-6' method, significantly reducing operational complexity compared to traditional methods. Furthermore, this work proposes a ludic and experimental path toward the prime-counting function π(n), allowing students to intuitively discover the distribution of primes and Legendre's constant, connecting fundamental concepts of number theory with modern programming.