Category Archives: primes

Factorization diagram cards are here!

Posted on September 11, 2016 by

It’s been a long process, but factorization diagram cards are finally available for purchase! If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading. History As … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 2 Comments

Factorization diagram card redesign: feedback welcome!

Posted on August 24, 2016 by

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!

Posted on May 31, 2016 by

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 →

Posted in arithmetic, counting, pattern, pictures, primes, teaching, video | Tagged , , | 5 Comments

MaBloWriMo 16: Recap and outline

Posted on November 17, 2015 by

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 →

Posted in algebra, arithmetic, computation, famous numbers, group theory, iteration, modular arithmetic, number theory, primes | Tagged , , , , , , , , , | 2 Comments

MaBloWriMo 6: The Proof Begins

Posted on November 7, 2015 by

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 →

Posted in algebra, arithmetic, computation, number theory, primes | Tagged , , , , , , , | 1 Comment

MaBloWriMo 5: The Lucas-Lehmer Test

Posted on November 6, 2015 by

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 →

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

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

Posted on November 5, 2015 by

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 →

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