Prime Numbers Study Using Computational Methods

Prime Numbers Study Using Computational Methods

Khaled Mahmoud Al-Hamad, Mahmoud Mansour,

The Jubilee School, Amman, Amman, JORDAN

Prime numbers have intrigued curious thinkers for centuries, and this research project will focus on studying various properties of primes and continue some unfinished researches on this field. It`s really important to study the prime numbers because they have many practical applications in our life, like in cryptography, and computer security.

Computational methods were used to accomplish the study; three independent programs were made, the first two studied primes` various aspects, like distribution, density, behavior, frequency, infiniteness along with many others, while the third program was focused on studying and proving the GoldBach conjecture. After that data was collected from each of the three programs, and an insight look at prime related books was taken. And finally the data was organized and an independent research on the result of each of the three programs was written.

In accord to the Prime Spiral software, the prime numbers tends to favor some diagonal lines than others, the research proved that each of these lines is infinite, and that these lines keep appearing even with a different midpoint. Also the Prime Spiral software can be used to draw any other types of numbers (not just primes), like perfect, triangular, square, abundant along with many others. The Prime Line software, showed that primes are infinite and that the increase in primes tends to become more linear as the drawn interval gets larger. The Goldbach Conjecture Simulator software managed to give a graphical proof that this conjecture is true(Results are more detailed in the research paper)

Finally, this research demonstrates what already existed, it adds to the previous, yet it finds out the new, and each of the three programs could be further investigated to gain more results.