Exploration and Classification of Prime Numbers: A Systematic Approach | Book Publisher International

 

The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposed prime numbers and we noted it Esp.

 

We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 are: 2; 4: and 6.

 

For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime.

 

For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say, two cousin prime numbers, are successive.

 

For those whose difference is equal to 2, we showed their origin We made an observation on the supposed prime numbers then we established two pairs of equations from this observation we deduced the origin of the Mersenne number and that of the Fermat number We subsequently established from the set of supposed prime numbers the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted Enp. We then extracted from the set of supposed prime numbers the numbers which are not prime and the set of remaining numbers constitutes the set of prime numbers denoted Ep. We have deduced from the previous set, the set of prime numbers between two integers, We have shown the class of prime numbers, We have explained during our demonstrations the structure of the chain of prime numbers.

 

Author(s) Details

Mady Ndiaye

Middle School Badara Mbaye Kaba, Dakar academy inspection, Ministry of National, Education of Senegal, Dakar, Senegal.

 

Please see the link:- https://doi.org/10.9734/bpi/mono/978-81-976932-5-0