Integer Factorization Is Not in P: Logical Proof

EasyChair Preprint 12579, version 2

Abstract

In  this  research  paper,  the  problem  of   testing   whether a  given  integer  is  Highly  Composite  Number  is  formulated.  Using  Ramanujan's   Theorem,  it  is  reasoned  that  the  unique  factorization  of  Highly  Composite  Number  cannot  be  performed  using  a  polynomial  time  algorithm.  Since  the  class  of  Highly  Composite  Numbers  is  countably  infinite,  integer  factorization  is  NOT  in  class  P.

Keyphrases: Highly Composite Numbers, polynomial-time algorithm, prime numbers, unique factorization

@booklet{EasyChair:12579,
  author    = {Rama Garimella},
  title     = {Integer Factorization Is Not in P: Logical Proof},
  howpublished = {EasyChair Preprint 12579},
  year      = {EasyChair, 2024}}