We just completed another project in math class that involved the Dot product and twin primes. My students learned how to multiply two vectors together using the Dot product and I wanted to give them some more practice. Since we have previously studied the prime numbers, I thought it would be interesting to link the two together. This time I wanted to use the prime numbers but to also use something a little more interesting. I thought the twin primes, primes that differ by two, would make an interesting project. We have already used the first 100 primes in our Order of Operations project so to make it interesting, we used twin primes of six digit length that begin with a 77.

Here is what a calculation looks like for a set of large twin primes.

So 774,797 = 2(300,779) + 15,749(11), and its twin 774,799 = 2(301867) + 34213(5). These calculations are underneath of the drawing or image of each prime. As you can see, all four of the numbers in the two vectors are also prime numbers.

That was one of the requirements for this project:

*For each vector, find two prime numbers such that the Dot product is one of your assigned Twin Primes.*

The project took the class about a week to complete as each student was given three twin primes to complete, for a total of six prime numbers each. Some students used the free app Is It Prime to help determine is their factor was prime or not. This app was found to be much quicker that a printout list of the primes.

One of the more interesting primes was 771887. The first two digits, 77, is my favorite number and the rest,1887, is the year the great mathematician Ramanujan was born.

The completed poster shows all the students’ creative work on the covers and the the calculations underneath. Some of the primes were very difficult to calculate, but this gave the opportunity for some students to step up and help out, which they did.

Here is the completed poster project. Notice also that each row has six entries and each prime number is six digits long. Six is the first perfect number and that gave me the idea to use six digit primes.

I’m always amazed what my students come up with in terms of combining art and mathematics. A project like this helps them to recognize patterns and appreciate the beauty in numbers and also brings out their creativity which helps them sharpen their problem solving ability.

Our next project will probably involve matrices and determinants somehow connected to perfect or prime numbers. I’ll try and make some interesting connection.

### Kevin

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