Collatz Conjecture Proof for Special Integer Subsets and a Unified Criterion for Twin Prime Identification

EasyChair Preprint 11389

Abstract

This paper presents a proof of the Collatz conjecture for a specific
subset of positive integers, those formed by multiplying a prime number
”p” greater than three with an odd integer ”u” derived using Fermat’s
little theorem. Additionally, we introduce a novel screening criterion for
identifying candidate twin primes, extending our previous work linking
twin primes (p and p+2) with the equation 2(p−2) = pu+v, where unique
solutions for u and v are required. This unified criterion offers a promising
approach to twin prime identification within a wider range of integers,
further advancing research in this mathematical domain.

Keyphrases: Prime, Real, natural number

@booklet{EasyChair:11389,
  author    = {Budee U Zaman},
  title     = {Collatz Conjecture Proof for Special Integer Subsets and a Unified Criterion for Twin Prime Identification},
  howpublished = {EasyChair Preprint 11389},
  year      = {EasyChair, 2023}}