Numbers That Should Be Prime

This is the first part of an ongoing series about more modern ideas and topics in mathematics that aren’t in mathematics curricula, K-12, but could be. and should be. Much of what we call “school mathematics” is between 200 and 400 years old, if not older.

Prime numbers are in some mathematics curricula, but usually they just appear in the context of prime factoring. Wondering if a number is prime is one of the most interesting things we can do with numbers, and our students can do it as soon as they learn about odds, evens, skipcounting, and a little bit about multiplication.

Googling “numbers that should be prime” does not turn up what I want. It does not show me numbers ending in 1, 3, 7, or 9 that look like they, by all rights, *should* be prime. Number that give you that “prime feeling” as it were.

I am thinking of when you see a number, an odd number, and you think:

that looks prime.

I think 737 looks prime. 101, 1001, 10001-they all look prime. 91 looks prime, at first glance, until you find out that 7 x 13 is 91.

Here is a simple prime number checker, if you want to play with some numbers.

Here is a game called “Is It Prime?” that fires smaller numbers at you, and you decide if they are prime or not:

Quick: is 129 prime? It kind of has the…look. But: it factors out to 3 x 43. As numbers get bigger, you have to filter for bigger and bigger primes. Think back to 91: 13 comes into play as a factor.

Let’s try some more:

10 003. Looks prime? Why not? But what hidden larger primes could be factors?

Wow. It is actually 7 x 1429. You can see why it takes a lot of computational work to find increasingly larger and larger primes.

With young kids, you can just start with a hundreds square, and do a simple sieve, the Sieve of Eratosthenes.

If you sieve out all multiples of 2, 3, 5, and 7, you get this:

Humans are great at finding patterns, but I defy you to find a pattern in there. Or is there one? Crack that code, and you could win fame and money.

In classrooms, though, it’s not about fame and money: it’s about playing with numbers, because it is pleasurable to play with numbers. It is fun to break numbers down to their atomic bits, which we call prime numbers.

After all, mathematics should surprise, and mathematics should be full of wonder. Let’s inscribe surprise, wonder, and playing with numbers in mathematics curricula worldwide.

Matthew Oldridge is an educator, writer, and “thinker about things”. I can be found on Twitter: Matthew Oldridge

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