Category Archives: primes

Animated Sieve of Eratosthenes

Posted on April 11, 2013 by

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 , , , , | 11 Comments

Factorization diagram cards: help?

Posted on February 5, 2013 by

The other day I got a lovely email from Malke Rosenfeld thanking me for creating factorization diagrams and linking me to her blog post about “factor dominoes”: she printed out some factorization diagrams, glued them to cardstock, and used the … Continue reading →

Posted in arithmetic, pictures, primes | Tagged , , , | 2 Comments

Mersenne primes and the Lucas-Lehmer test

Posted on January 17, 2013 by

Mersenne numbers, named after Marin Mersenne, are numbers of the form . The first few Mersenne numbers are therefore , , , , , and so on. Mersenne numbers come up all the time in computer science (for example, is … Continue reading →

Posted in arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes | Tagged , , , , | 3 Comments

More factorization diagrams

Posted on November 5, 2012 by

My post on factorization diagrams from a month ago turned out to be (unexpectedly) quite popular! I got ten times as many hits as usual the day it was published, and since then quite a few other people have created … Continue reading →

Posted in arithmetic, links, pictures, primes, programming, recursion | Tagged , , | 15 Comments

Factorization diagrams

Posted on October 5, 2012 by

In an idle moment a while ago I wrote a program to generate "factorization diagrams". Here’s 700: It’s easy to see (I hope), just by looking at the arrangement of dots, that there are in total. Here’s how I did … Continue reading →

Posted in arithmetic, pictures, primes, programming, recursion | Tagged , , | 72 Comments

Book Review: The Enigma of the Spiral Waves

Posted on July 14, 2012 by

The Enigma of the Spiral Waves (Secrets of Creation Volume 2)words by Matthew Watkins, pictures by Matt Tweed Matthew Watkins and Matt Tweed have done it again! I previously wrote a (very positive) review of Volume I—this book is just … Continue reading →

Posted in books, open problems, primes, review | Tagged , , | 1 Comment

Fun with repunit divisors: more solutions

Posted on November 17, 2011 by

In Fun with repunit divisors I posed the following challenge: Prove that every prime other than 2 or 5 is a divisor of some repunit. In other words, if you make a list of the prime factorizations of repunits, every … Continue reading →

Posted in arithmetic, iteration, modular arithmetic, number theory, primes, programming, proof, solutions | Tagged

Fun with repunit divisors: proofs

Posted on November 16, 2011 by

As promised, here are some solutions to the repunit puzzle posed in my previous post. (Stop reading now if you don’t want to see solutions yet!) Prove that every prime other than 2 or 5 is a divisor of some … Continue reading →

Posted in iteration, modular arithmetic, number theory, pattern, primes, proof | Tagged , , , , | 1 Comment

Fun with repunit divisors

Posted on November 11, 2011 by

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

Triangunit divisors and quadratic reciprocity

Posted on March 20, 2011 by

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading →

Posted in arithmetic, modular arithmetic, number theory, primes, proof | Tagged , , , , | 5 Comments