My Prime Factorization Cardigan

I did it! More than two years after beginning, I have finally completed my Prime Factorization Cardigan!

Wearing cardigan1

Here’s how it works! The stripes each represent a counting number. They go from left to right, cuff to cuff. 1 is black, the background color (which is a factor of everything). Then each prime gets a new color. 2 is blue; 3 is pink; 5 is yellow; 7 is purple….

Composite numbers get the combination of colors for their factors. 6 = 2 x 3, so it’s alternating blue and pink. 10 = 2 x 5, so blue and yellow. 12 = 2 x 2 x 3, so two stitches of blue followed by one of pink….

Perfect powers get multiple rows. 4 = 2 x 2, so two rows of blue; 8 = 2 x 2 x 2, so three rows of blue; 9 = 3 x 3, so two rows of pink. I think my favorite is 36 = 2 x 2 x 3 x 3, so I did two rows of alternating blue and pink.

I put labels in one picture, to give the pattern:

Labeled Cardigan1-18

As for details, I used Plymouth Encore yarn, 75% acrylic, 25% wool — it is not expensive and comes in many colors. I looked online for a pattern knitted cuff-to-cuff, and found this Rainbow Lace Jacket. I of course changed the colors. I knitted the stripes in garter stitch, and the rows in between the stripes in black stockinette.

And now for more pictures! First, an overall look at the sweater again:

PF Cardigan Front

And with the arms down:

PF Cardigan arms down

And the back: (I decided to make the numbers go two-dimensionally across the sweater, from cuff to cuff. So the back is a mirror of the front.)

PF Cardigan Back

And here’s more detail, Numbers 17 to 32 (The powers of 2 are easy to spot! They are the multiple rows of blue.):


Then Numbers 26 to 38:


34 to 47:


41 to 58:


51 to 63:


And finally, 64 to 78:


There you have it! The latest in my prime factorization knitting adventures. Let’s see, I feel compelled to summarize what I’ve done.

It began with the Prime Factorization Sweater.


Then when that became wildly popular on the internet, I made a Prime Factorization T-shirt. (These are available for sale, by the way.)

Twitter Profile

I experimented with stripes when I made my Prime Factorization Scarf, and planned out how to do this cardigan.

Prime Factorization Scarf

Then my siblings were expecting babies. For my sister’s baby, I knitted a Coded Blessing Blanket.

Blessing Blanket

For my brother’s baby, nothing but a Prime Factorization Blanket would do.


Which got me going on a Pascal’s Triangle Shawl.


Which got me to start another, prettier one (Still not finished).

Pascals Colors

And brings me back to the Prime Factorization Cardigan!

Wearing cardigan hands down

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


  1. I teach future teachers and just emailed all of them this website! This is exactly what we talk about in class. How cool 🙂

  2. These are fabulous! Reminds me of the mathematical quilts by Diana Venters and Elaine Ellison. Their quilts were on display in Rock Hill, SC many years ago. And when I was a student at Winthrop University, Ms. Venters came to finish a course for a teacher that passed away and she shared her love of teaching and displaying math visually. I have carried that appreciation with me ever since. I wish I had the talent and creativity for such projects.
    I will be looking for those tshirts for sale. I love it!
    Thanks for sharing what you do. Kudos!

  3. Again, this is amazing! Those details! I’m glad I discovered your website, it goes right into my feed for inspirational reads. Love it!

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