Note for the Millennium Prize Problems

EasyChair Preprint no. 11927, version history

VersionDatePagesVersion notes
1January 31, 202411
2February 1, 202411

We use the 1-in-3 3sat problem

3February 2, 202411

We created a Github repository with the software solution in Python

4February 3, 202411

We show that the Monotone Weighted Xor 2-satisfiability problem ($MWX2SAT$) is $NP$-complete and $P$ at the same time.

5February 6, 202411

We improved the Lemma 3

6March 10, 202411

We changed the abstract and content

7March 14, 202412

We improved the content.

8March 15, 202411

In the previous version, we create two ways to prove that MWX2SAT is in P. In this version, we remove the one that is flawed and we keep the correct and single one.

9March 28, 202413

Added the Discussion section

10April 8, 202413

We replaced in the definition of the K-CLOSURE the content "($u \in V'$ or $v \in V'$) or ($u \notin V'$ or $v \notin V'$)" by "($u \in V'$ and $v \in V'$) or ($u \notin V'$ and $v \notin V'$)"

Keyphrases: complexity classes, computational complexity, elementary number theory, polynomial time, prime numbers, Riemann hypothesis

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@Booklet{EasyChair:11927,
  author = {Frank Vega},
  title = {Note for the Millennium Prize Problems},
  howpublished = {EasyChair Preprint no. 11927},

  year = {EasyChair, 2024}}