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A remark on large even integers of the form $p+P_3$

Runbo Li

Abstract

Let $N$ denotes a sufficiently large even integer, $p$ denotes a prime and $P_{r}$ denotes an integer with at most $r$ prime factors. In this paper, we study the solutions of the equation $N-p=P_3$ and consider two special cases where $p$ is small, and $p,P_3$ are within short intervals.

A remark on large even integers of the form $p+P_3$

Abstract

Let denotes a sufficiently large even integer, denotes a prime and denotes an integer with at most prime factors. In this paper, we study the solutions of the equation and consider two special cases where is small, and are within short intervals.
Paper Structure (3 sections, 6 theorems, 32 equations)

This paper contains 3 sections, 6 theorems, 32 equations.

Table of Contents

  1. Introduction
  2. Preliminary lemmas
  3. Proof of Theorem 1.1

Key Result

Theorem 1.1

for $0.838 \leqslant \theta \leqslant 1$ and $0.919 \leqslant \kappa \leqslant 1$, we have

Theorems & Definitions (7)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • proof