Prime Approximation

The proposed formula provides an approximation for the nth prime number, where n represents the position of the prime in the ordered sequence of all prime numbers. Instead of determining primality directly, the formula estimates the numerical value of the prime corresponding to a given index n. The use of the greatest integer function ensures an integer output, while the ±1 adjustment accounts for small deviations caused by rounding. This approach emphasizes simplicity and computational ease, making it suitable for quick estimation and educational exploration of prime number growth.