Number Theory

In 1932, a leading authority on rattlesnakes, Laurence Klauber, discovered a startling pattern within a triangle of primes.

What do you call two prime numbers who are very close together?

Can any even number be written as the sum of two primes? Goldbach thought so, but we haven’t proven it… yet!

Why does the sum of the first 5 odds also equal 5 squared?

Pascal’s pattern-packed triangle is a potent puzzle for pupils to ponder.

How can you cross each bridge in this city exactly once?

Can any perfect square be written as the sum of two primes?

What if we make a huge spiral of numbers and then highlight only the primes? Well, a bunch of weird patterns show up!

Prime numbers are unpredictable! How can we possibly find them all? An Ancient Greek mathematician found one way!

Can you make each side of this triangle add up to 9 using the digits 1-6?

The Collatz Conjecture: start with any number and get to 1 using just two rules. It seems to always work…

Every positive integer can be written as the sum of (at most) four perfect squares!

Imagine a 3×3 square in which every row, column, and diagonal have the same sum. That’s a magic square!

It seems like there’s always a prime number between two perfect squares… but is this always the case!?

No video gets me more email from students! How few colors can you use to color in any map so that no two, neighboring regions are the same color?

Using this one weird trick, it seems that you can turn any number into a palindrome!

So, can you write every odd (greater than 3) as the sum of three primes?