Teorema de Geovanni

There was no way to calculate whether a number was prime or not, especially for large numbers, and it was even more complicated to know which was the prime number in the nth position.
Recently, I discovered a relationship between prime and non-prime numbers, managing to generate an algorithm that efficiently predicts whether a number is prime. With the help of interaction with AI, I refined and refined this idea, managing not only to predict whether a number is prime, but also to generate additional functions to predict which would be the prime number in the nth position, which would be the prime numbers in a given range, obtain all the prime numbers before a certain number, and graph all existing prime numbers, giving a limit.

My application generates all these calculations correctly, thus solving this important part of mathematics.

To achieve these calculations, I managed to find an efficient way to relate prime and non-prime numbers. I also took advantage of the sieve and used a self-learning algorithm to reduce the time by leveraging previous calculations. Furthermore, during the refining process, I managed to ensure that the algorithm only evaluates possible values ​​that could return True when performing calculations, thus ruling out a large number of variables, which reduces execution time.

Already testing and verifying the correct and efficient operation of the system with the help of interaction with AI, I created a theorem to predict whether a number is prime or not, on which my entire algorithm is based (Geovanni's Theorem).

I hope this contribution will be significant and a useful tool in the field of mathematics. Once the problem is defined, the prime relationship can be clearly seen and verified. This could be an NP problem since if I give you the answer, you can easily verify that it is correct, but you cannot easily find that answer.

EFFICIENCY:
- Complexity: O(√n / log n) using smart screening
- Self-learning: Expands knowledge with each calculation
- Minimal verification: Only prime divisors are necessary
- Works for all natural numbers

Without further ado, I'll sign off and share my theorem "Geovanni's Theorem for Prime Numbers" and the link to access the code on Github.

Geovanni's Theorem (2025)

A number N > 1 is prime if and only if:
N ∈ P ∨ (∀f ∈ P, N mod f ≠ 0)
where P = {primes ≤ √N}

Author: Geovanni Burgos
email: adelantado610@gmail.com
cell phone: +52 9993343443
Ucu Yucatan 10/10/25

link to code:

https://github.com/principe610/Teorema_de_geovanni_para_numeros_primos.git