# A Sieve for Twin Primes

## TL;DR

This paper introduces a new sieve algorithm for twin primes, provides heuristic estimates for their counts, and compares these estimates with actual data, offering a simpler correction factor than previous methods.

## Contribution

The paper presents a novel sieve algorithm for twin primes and introduces a simpler heuristic correction factor for estimating their distribution.

## Key findings

- The sieve algorithm effectively generates twin primes.
- Heuristic estimates closely match actual counts up to 8009.
- A new correction factor simplifies twin prime distribution estimates.

## Abstract

We present an algorithm analogous to the sieve of Eratosthenes that produces the list of twin primes. Next, we count the number of twin primes resulting from the construction with two different heuristic arguments. The first method is essentially the same as the one in Hardy and Wright. However, the second method is novel. It results in the same asymptotic formula but it uses a simpler correction factor than theirs. Though we have no theory for the accuracy of our estimates, we compute them both without and with the correction factor and they turn out to be close to the actual counts up to 8009.