An #Exact #Formula for the #Primes: #Willans' Formula - YouTube

I didn't know this formula existed. It was published in 1964 but if you look at it carefully, it's not a formula as such, it's actually an #algorithm coded into some nifty #maths. It gets excruciatingly slow for even modest values on n, when n represents the nth prime. I've written it as a #maxima code below.

https://www.youtube.com/watch?v=j5s0h42GfvM

#WillansFormula #Mathematics #PrimeNumbers

prime(n):=1+sum(floor((n/sum(floor(cos(%pi*(factorial(j-1)+1)/j)^2),j,1,i))^(1/n)),i,1,2^n);

https://www.noulakaz.net/2007/03/18/a-regular-expression-to-check-for-prime-numbers/

#computers #math #primenumbers

Mathematical recreation

Why do prime numbers make these spirals?

I came across this video some weeks ago, perhaps right here on Pluspora (if so, I apologize for failing to credit the person who first posted it).

If you have any interest in number theory, this video is a jewel.

If you have no interest in number theory, this video will show you the error of your ways ;-)

It is at once fascinating and completely understandable, and it clears up a mystery which turns out to be no mystery at all. (Such is the way with pure math: Everything is the way it is because logically it simply could not be any other way. And when you discover why it must be as it is, it is deliciously, orgasmically obvious.)

#Math #PureMath #NumberTheory #PrimeNumbers #Integers #RealNumbers #IntegersVsReals

https://www.youtube.com/watch?v=EK32jo7i5LQ