Category Archives: primes

Factorization diagram card redesign: feedback welcome!

After getting a printed set of factorization diagram cards, I decided there were a few design tweaks I wanted to make. I’ve gone through a few iterations and I think they are definitely better now. Here are some representative samples … Continue reading

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 6 Comments

Factorization diagram cards!

I’ve designed a set of factorization diagram cards and had them actually printed. This is one of the first times in my life when I have caused Actual Physical Objects to be created (other than using a printer I guess) … Continue reading

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MaBloWriMo 16: Recap and outline

We have now established all the facts we will need about groups, and have incidentally just passed the halfway point of MaBloWriMo. This feels like a good time to take a step back and outline what we’ve done so far … Continue reading

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MaBloWriMo 6: The Proof Begins

Today we’re going to start in on proving the Lucas-Lehmer test. Yesterday we saw how, given a Mersenne number , we can define a sequence of integers , with the claim that if and only if is prime. We’re going … Continue reading

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MaBloWriMo 5: The Lucas-Lehmer Test

We now know that can only be prime when is prime; but even when is prime, sometimes is prime and sometimes it isn’t. The Lucas-Lehmer test is a way to tell us whether is prime, for any prime . The … Continue reading

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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

Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes | Tagged , , , , , , | 1 Comment