Primes in tuples and Romanoff's theorem

TL;DR

This paper establishes a lower bound on the number of primes within tuples and applies this result to derive bounds for Romanoff's theorem related functions, advancing understanding of prime distributions.

Contribution

It provides a new lower bound for primes in tuples and applies it to Romanoff's theorem, offering novel insights into prime representations.

Findings

Lower bound for primes in tuples

Lower bound for Romanoff type representation functions

Enhanced understanding of prime distribution in tuples

Abstract

We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.