Brian Claassen, Dr. Brian Sittinger, & Dr. Ivona Grzegorczyk
This project is on the subject of twin prime numbers in Number Theory. These are pairs of primes whose pairwise difference is two, for example 5 and 7 are twin primes. There are infinitely many prime numbers, many come as a twin pair. We show examples of such pairs when the numbers are quite large. The main question is if there are infinitely many such pairs? We prove several facts concerning prime numbers, including some results related to twin primes. One of the interesting statements that was proven quite recently says that there is infinitely many pairs of primes with relatively small gaps between them (however, currently these gaps are much larger than 2). At this time it is still no proof or methodology to find infinitely many pairs of twin prime numbers. We. explain the current situation on this topic and give history of the study of pairs with fixed gaps between them.