### Prime numbers and new regularities

Student

School

City

: Rina Ismailati

: Ismail Qemali

: Tiranë

This mathematical project is about prime numbers. It discovers new regularities in them. Except the algebraic proceedings, I’ve also built new, interesting and regular graphics for each prime number that I’ve studied.

In fact, this project includes a wider specter than prime numbers, because the regularities discovered in them, are present even in some other numbers, which are made of prime numbers. For example, the nr 34.(17 x 2). The regularities discovered in the nr 17, are also present in the nr 34. I’ve studied only a few prime numbers, but this studying method can be applied to any other prime number.

More details: this project has to do with the division of integers with prime numbers. The conclusion in this project is that we can find regularities in the numbers that come after the decimal point, they are not chaotic. Also, we can create graphics by linking the numbers of the periods of this divisions, with the remainders of the devisions. Each prime number has its own graphic.

For example: the number 7. Let's study: 1:7, 2:7, 3:7, 4:7, 5:7, 6:7. The period of these divisions is the same. What’s different about them is only the numbers that comes after the decimal point, so the first number of the period. We can find regularities even inside of one period, even if we put these 6 periods in a column. (these regularities are repeated in cyclic way for every 6 numbers that are divided by 7).

Another point of the project is about the nr 9,in what way this number can be found “inside” every number.