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If you are interested in learning more about python and caching I wrote a post about it couple days ago:

That's more accurately described as memoization, as caching is a broader term.

Also, you might want to look into Sieve of Eratosthenes, as you only have to test up to sqrt(n) for primality: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Thank you, AncientPC. I have adjusted the article with the insight you and many others have provided me.