Download PDFOpen PDF in browserA Mathematical Conjecture from P versus NPEasyChair Preprint 34155 pages•Date: May 16, 2020AbstractP 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 NPcomplete. To attack the P versus NP question the concept of NPcompleteness has been very useful. If any single NPcomplete 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 NPcomplete problem Subset Product is in P and thus, the complexity class P is equal to NP. Keyphrases: completeness, complexity classes, logarithm, polynomial time, tuple
