I started my first IB Mathematics project last week. It involves the twin primes. A **twin prime** is a prime number that has a prime gap of two. An example is the twin prime of 11 and 13.

The first few twin primes are:

(3,5), (5,7), (11,13), (17,19)…

(2,3) is not considered a twin prime because they do not differ by 2. It is not known if there are infinitely many twin primes. See the Twin Prime Conjecture.

A major result in 2013 by Yitang “Tom” Zhang, a little known but popular math professor at the University of New Hampshire, proved the “bounded gaps” conjecture about the distribution of prime numbers.

Because prime numbers are fundamentally connected with multiplication, understanding their additive properties can be tricky. Some of the oldest unsolved problems in mathematics concern basic questions about primes and addition, such as the twin primes conjecture, which proposes that there are infinitely many pairs of primes that differ by only 2, and the Goldbach conjecture, which proposes that every even number is the sum of two primes. Read more at Quanta

The challenge for this project is to take the digits in the year 1-9-9-8 and using only those digits and order of operations, produce the first fifty pairs of twin primes. You can use any integer for an exponent and also use factorial. So for example, 3! = 6, and 4! =24.

I’ll post some pictures of the mathematics in the next post on this project.

We are about half way through with the mathematics of the project and they are starting to make the poster. It’s fun to try to come up with combinations of numbers to try to get to each prime. I hope this leads us deeper into the study of the twin primes. I’ll have an update next week on the project.

### Kevin

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