Is the Sieve of Eratosthenese past its prime?
Channel: Ben Peters Jones
Date: 2021-08-26

The Sieve of Eratosthenes is an amazing tool for teaching people about prime numbers and composite numbers but it's not without its limitations. I've tried to answer the question, 'Is there a better way of representing a sieve like this?'

0:00  Sieve of Eratosthenes
In the first part of this video I give a quick recap of the standard Sieve of Eratosthenes on a 10x10 grid/table/array. 
1:22 Sieve of Eratosthenes with dynamic widths
I then attempt at representing the Sieve of Eratosthenes in the best light.
4:50 Square Sieve
I've then attempted to create a sieve that has fewer limitations than the Sieve of Eratosthenes. I set up the sieve which is essentially a visualisation of the difference of two square numbers. I then also talk about: 
* Which numbers can be represented as the difference of two squares
* How the sieve relates to trial division
* Creating a primality test from the difference of two squares
* Setting a lower and upper bound for where those square numbers are.
15:07 Outro

This is the first in a series of videos aiming to improve the simple sieve that's at the start of every prime number journey. The next videos in the series can be watched in any order but look at modularity, using modularity to optimise the primality test, primes in quadratic progression and twin primes, and a looking at increasing the probability of finding prime number. https://www.youtube.com/watch?v=g7DWrO19CNY&list=PLhMQ5JG0CnKmfTIpKLAVspEfqhnjRoRVH&ab_channel=BenPetersJones

I'm not a mathematician and there's every chance that something I've said is wrong. If that's the case, please let me know and I'll try to fix it.

This video series is my entry to the 3Blue1Brown Summer of Maths Exposition competition in August/September 2021.