I finished it! Last week, I finished sewing the ends in on my new Prime Factorization Scarf.

The scarf is similar to my Prime Factorization Sweater, using a new color for each prime factor. For the scarf, though, instead of making a grid of squares representing each number, I used two-row stripes for each factor. I separated each number with two rows of black, which represented the number 1 (since 1 times anything doesn’t change the value.)

I like the way the scarf gives the flow of the numbers. You can look closely at the blue color for 2 and watch it repeat. Then notice how the pink color for 3 repeats a little more slowly. And 5 a little more slowly than that. The scarf goes all the way up to 50.

Here are some sections up close. First, this picture shows 1 through 21:

2 is blue.

3 is pink.

4 = 2 x 2, so it’s two stripes of blue.

5 is yellow.

6 = 2 x 3, so it’s a stripe of blue and a stripe of pink.

7 is purple.

8 = 2 x 2 x 2, so it’s three stripes of blue.

9 = 3 x 3, so it’s two stripes of pink.

10 = 2 x 5, so it’s a stripe of blue and a stripe of yellow.

11 gets a new color, green.

12 = 2 x 2 x 3, so it’s two stripes of blue and a stripe of pink.

And so on….

Here is a picture showing 17 (light pink) through 35:

And finally, 33 to 50:

My earlier posts explained why I chose the pattern I did. I wanted the scarf to be reversible, but it’s not quite as easy to read as plain garter stitch stripes.

What’s next? A cuff-to-cuff cardigan! Only, I want to go higher than 50, so I decided to combine factors in one stripe — unless you have perfect powers of a number. Here’s a preview. I’m working on 33 now. (You can see that since 32 = 2^5, it’s 5 rows of blue.) It’s going to be flamboyantly bright, but I plan to wear my primes with pride!

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

Tags: mathematical knitting, prime factorization, Prime Factorization Scarf

[…] of course, I went back to talk to Stephon Alexander more. And this time, I had my prime factorization scarf with me. And the Outliers Scarf, for which I’m sewing in the […]

[…] But since then, I’ve designed a t-shirt for sale to all on Cafepress. I’ve knitted a scarf that uses color-coded stripes to represent the prime factorization of numbers up to 50. And […]