Tag Archives: primes

The Riemann zeta function and prime numbers

Posted on March 6, 2017 by Brent

In a previous post I defined the famous Riemann zeta function, Today I want to give you a glimpse of what it has to do with prime numbers—which is a big part of why it is so famous. Consider the … Continue reading →

Posted in number theory | Tagged , , , , | 15 Comments

The Riemann zeta function

Posted on February 2, 2017 by Brent

Recall from my previous post that given a function , we define , the Dirichlet generating function of , by We also proved that : the product of Dirichlet generating functions is the Dirichlet generating function of the Dirichlet convolution. … Continue reading →

Posted in number theory | Tagged , , , , , , , | 2 Comments

Dirichlet generating functions

Posted on January 30, 2017 by Brent

Suppose is a function defined for positive integers . Then we can define an infinite series as follows: (This might look a bit strange, but bear with me!) For example, suppose for all . Then (Note that in this case, … Continue reading →

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

Animated Sieve of Eratosthenes

Posted on April 11, 2013 by Brent

Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.) Can you figure out what’s going on? The source code for the animation is here; I was inspired by … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, video | Tagged , , , , | 12 Comments

Fun with repunit divisors

Posted on November 11, 2011 by Brent

In honor of today’s date (11/11/11), here’s a fun little problem (and some follow-up problems) I’ve seen posed in a few places (for example, here is a very similar problem). If I recall correctly, it was also a problem on … Continue reading →

Posted in arithmetic, challenges, modular arithmetic, number theory, primes | Tagged , , | 16 Comments

Prime Time in Haskell

Posted on January 6, 2011 by Brent

In a recent blog post, Patrick Vennebush of Math Jokes 4 Mathy Folks noted that 2011 can be expressed as a sum of consecutive prime numbers, and challenged his readers to work out how. He also posed a couple further … Continue reading →

Posted in arithmetic, number theory, primes, programming | Tagged , , , | 8 Comments