Ode to Twin Primes

Twin primes are a special kind of prime numbers, divided by only one even number. However, they are unfamiliar to most people. We wanted to make twin primes memorable by dedicating a poetry collection to them.

Scientific background and basis for the poems:

Prime numbers are numbers that can only be divided by 1 and itself. Formulated the other way around: a prime is a number that cannot be formed by multiplying two smaller numbers. Opposite to prime numbers are composite number, the ‘regular’ numbers which can be formed by multiplying smaller numbers, and can also be divided by these smaller number. Moreover, there are infinitely many prime numbers, as Euclid already proved in 300 BC (Saidak, 2006). The distribution of primes is random, but the greater the number, the less change for it to be a prime, according to the Prime Number Theorem (Bateman & Diamond, 1996).

If p is a prime number, and p + 2 is also a prime number, then p and p + 2 are twin primes. The distance between two prime numbers is called the gap between primes (Polymath, 2014). For twin primes, the gap between primes is thus 2. Twin primes seem to be even more randomly distributed than regular primes (Brent, 1975) and also more uncommen (Polymath, 2014).

Their infrequency makes twin primes even more exceptional than regular primes in our eyes. However, we feel they are not as known as regular primes. When we explored this field and asked around in our groups of family and friends, nobody seemed to know twin primes! That is why we decided to dedicate our project to twin primes.

We feel sorrowful for twin primes because they will always be almost together but separated by one even number. Therefore, we wanted to write a collection of poems to honour them. We chose the title Ode to Twin Primes to underline the praising of the twin primes. We decided not to include any images in the booklet to really focus on the solitude of the twin prime numbers.

We think twin primes can be compared to star-crossed lovers, like Romeo and Juliet. In the poem dedicated to this, Romeo and Juliet, we draw this comparison. Both are destined to be together but are separated by contextual factors. For Romeo and Juliet, the families kept them apart, for twin primes the even number in between. The end of the poem refers to the randomness of which twin primes exist, which is as random as our choice of love can be sometimes.

True love is about how rare and random twin primes are (Polymath, 2014). According to Brun’s theorem (Brun, 1919), you might look for another twin prime at some point and never find one again, since he proved that there are finite number of twin primes. However, the Twin Prime Conjecture thinks there are infinitely many primes, however this has not yet been proved (Garcia, Kahoro, & Luca, 2019). We compare twin primes to real love in this poem, since real love is also rare to find.

To the moon and back compares prime numbers to stars, because both are very far apart (Bateman & Diamond, 1996). Moreover, if prime numbers are stars, then twin primes could be compared to a planet and its moon. Staying together by gravity, but not colliding because of speed and distance. They are seen as belonging together.

The Haiku in the middle booklet describes in written and in displayed from the distance between two twin primes. The word emptiness is spaced very far apart, as are the distances between two sequential regular primes. So, on one side of a twin prime is a big empty space until the next prime. However, on the other side of the twin primes is its twin prime very close by. The words close and near are spaced very narrowly.

Too far apart has been written for the endless love of two prime numbers, referring to the fact that they will always be together in the endless list of numbers. One of the numbers knows it has to look down upon his beloved one for all his life. The numbers will be close to each other, yet far away at the same time. It just is the destiny of their life.

Dear 70619 and 70621 is dedicated to two twin primes. 70619 and 70621 are asked whether they feel positive or negative about being a twin prime number. They are asked if they are doomed, blessed, happy, or just very sad. They are the odd ones out in a list of regular composite numbers, but they have each other at their side.

References

Bateman, P. T., & Diamond, H. G. (1996). A hundred years of prime numbers. The American mathematical monthly, 103(9), 729-741.

Brent, R. P. (1975). Irregularities in the distribution of primes and twin primes. Mathematics of Computation, 29(129), 43-56.

Brun, V. (1919). La série 1/5+ 1/7+ 1/11+ 1/13+ 1/17+ 1/19+ 1/29+ 1/31+ 1/41+ 1/43+ 1/59+ 1/61+... où les dénominateurs sont'nombres premieres jumeaux'est convergente ou finie. Bull. Sci. Math., 43, 124-128.

Garcia, S. R., Kahoro, E., & Luca, F. (2019). Primitive root bias for twin primes. Experimental Mathematics, 1-10.

Polymath, D. H. J. (2014). The" bounded gaps between primes" Polymath project-a retrospective. arXiv preprint arXiv:1409.8361.

Saidak, F. (2006). A new proof of Euclid's theorem. American Mathematical Monthly, 113(10), 937-938.

For the course Playful & Creative Science, we were asked to create different output for existing research. Melle Lefferts and I chose to make the research into twin prime numbers memorable by dedicating a self-written collection of poetry to twin primes.