Category Archives: primes

The Fermat primality test and the GCD test

Posted on November 18, 2018 by

In my previous post we proved that if shares a nontrivial common factor with , then , and this in turn proves that is not prime (by Fermat’s Little Theorem). But wait a minute, this is silly: if shares a … Continue reading →

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Making the Fermat primality test deterministic

Posted on November 17, 2018 by

Let’s recall Fermat’s Little Theorem: If is prime and is an integer where , then . Recall that we can turn this directly into a test for primality, called the Fermat primality test, as follows: given some number that we … Continue reading →

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Quickly recognizing primes less than 1000: memorizing exceptional composites

Posted on October 15, 2018 by

In my previous post I wrote about a procedure for testing the primality of any number less than : Test for divisibility by all primes up to , and also . (In practice I test for 2 and 5 first, … Continue reading →

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Quickly recognizing primes less than 1000: divisibility tests

Posted on October 11, 2018 by

I took a little hiatus from writing here since I attended the International Conference on Functional Programming, and since then have been catching up on teaching stuff and writing a bit on my other blog. I gave a talk at … Continue reading →

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Quickly recognizing primes less than 100

Posted on September 16, 2018 by

Recently, Mark Dominus wrote about trying to memorize all the prime numbers under . This is a cool idea, but it made me start thinking about alternative: instead of memorizing primes, could we memorize a procedure for determining whether a … Continue reading →

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Primality testing: recap

Posted on September 10, 2018 by

Whew, this is developing into one of the longest post series I’ve ever written (with quite a few tangents and detours along the way). I thought it would be worth taking a step back for a minute to recap what … Continue reading →

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The Fermat primality test

Posted on August 3, 2018 by

After several long tangents writing about orthogons and the chromatic number of the plane, I’m finally getting back to writing about primality testing. All along in this series, my ultimate goal has been to present some general primality testing algorithms … Continue reading →

Posted in computation, number theory, primes | Tagged , , | 5 Comments