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# Category Archives: primes

## MaBloWriMo 3: Mersenne composites in binary

Yesterday we saw that must be composite, since . Today I’ll talk about a somewhat more intuitive way to see this. Recall that we can write numbers in base 2, or “binary”, using the digits 0 and 1 (called “bits”, … Continue reading

Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
1 Comment

## MaBloWriMo: Mersenne composites

The name of the game is to find Mersenne numbers which are also prime. Today, a simple observation: can only be prime when is also prime. Put conversely, if is composite then is also composite. For example, is composite and … Continue reading

Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
1 Comment

## MaBloWriMo: The Lucas-Lehmer test

Today, I noticed both Zachary Abel and Qiaochu Yuan plan to write a blog post every day this month (hooray!). I haven’t written on here as much as I would like recently, and so I thought, why not? I already … Continue reading

Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
5 Comments

## Factorization diagram posters!

I’ve finally gotten around to making a nice factorization diagram poster: You can buy high-quality prints from Imagekind. (If you order soon you should have them before Christmas! =) I’m really quite happy with imagekind, the print quality is fantastic … Continue reading

Posted in arithmetic, counting, geometry, number theory, pattern, pictures, primes
Tagged diagrams, factorization, posters
7 Comments

## Animated Sieve of Eratosthenes

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 diagrams, Eratosthenes, primes, sieve, visualization
12 Comments

## Factorization diagram cards: help?

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

## Mersenne primes and the Lucas-Lehmer test

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 lehmer, lucas, Mersenne, prime, test
3 Comments