A Mathematical Conjecture from P versus NP

EasyChair Preprint 3415

Abstract

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. If any single NP-complete problem can be solved in polynomial time, then every NP problem has a polynomial time algorithm. We state the following conjecture for a natural number B greater than 3: The number of divisors of B is lesser than or equal to the quadratic value from the integer part of the logarithm of B in base 2. This conjecture has been checked for large numbers: Specifically, from every integer between 4 and 10 millions. If this conjecture is true, then the NP-complete problem Subset Product is in P and thus, the complexity class P is equal to NP.

Keyphrases: completeness, complexity classes, logarithm, polynomial time, tuple

@booklet{EasyChair:3415,
  author    = {Frank Vega},
  title     = {A Mathematical Conjecture from P versus NP},
  howpublished = {EasyChair Preprint 3415},
  year      = {EasyChair, 2020}}