body { -ms-overflow-style: scrollbar; overflow-y: scroll; overscroll-behavior-y: none; } .errorContainer { background-color: #FFF; color: #0F1419; max-width: 600px; margin: 0 auto; padding: 10%; font-family: Helvetica, sans-serif; font-size: 16px; } .errorButton { margin: 3em 0; } .errorButton a { background: #1DA1F2; border-radius: 2.5em; color: white; padding: 1em 2em; text-decoration: none; } .errorButton a:hover, .errorButton a:focus { background: rgb(26, 145, 218); } .errorFooter { color: #657786; font-size: 80%; line-height: 1.5; padding: 1em 0; } .errorFooter a, .errorFooter a:visited { color: #657786; text-decoration: none; padding-right: 1em; } .errorFooter a:hover, .errorFooter a:active { text-decoration: underline; } #placeholder, #react-root { display: none !important; } body { background-color: #FFF !important; }

JavaScript is not available.

We’ve detected that JavaScript is disabled in this browser. Please enable JavaScript or switch to a supported browser to continue using twitter.com. You can see a list of supported browsers in our Help Center.

Terms of Service Privacy Policy Cookie Policy Imprint Ads info © 2023 Twitter, Inc.

Conversation

An explicit formula for the prime numbers. Extremely clever. It essentially expresses a program as a function evaluation, using only very simple functions as building blocks.

An Exact Formula for the Primes: Willans' Formula

Formulas for the nth prime number actually exist! One was cleverly engineered in 1964 by C. P. Willans. But is it useful?----------------References:Herbert W...

9

21

166

At first I thought the cosine might be related to the prime counting function. It’s actually used to get an indicator variable for when its argument is an integer. The video explains.

Quote Tweet

In 1964, C.P. Willans found this exact(!) formula for the primes. Watch @ericrowland nicely explain how it works and why it's kinda useless... youtu.be/j5s0h42GfvM

10:00 AM · Oct 8, 2022

Replying to

And, what's the practical application for this?

1

Replying to

I use this same trick in one of the fizz buzz book solutions:

1

2