Category Archives: primes

MaBloWriMo 4: not all prime-index Mersenne numbers are prime

Over the past couple days we saw that if is composite, then is also composite. Equivalently, this means that if we want to be prime, then at the very least must also be prime. But at this point there is … Continue reading

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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

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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

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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 , , , , , , | 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 , , | 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 , , , , | 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

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