Exploration and Classification of Prime Numbers: A Systematic Approach


Author(s)
Mady Ndiaye
Middle School Badara Mbaye Kaba, Dakar academy inspection, Ministry of National, Education of Senegal, Dakar, Senegal.

ISBN 978-81-976932-5-0 (Print)
ISBN 978-81-976932-6-7 (eBook)
DOI: https://doi.org/10.9734/bpi/mono/978-81-976932-5-0

This work removed a poisonous thorn from under the feet of scientists by penetrating the secret causes of prime numbers.

Prime numbers posed many problems including the identification of a prime number, the class of a prime number, the origin of twin primes, the origin of cousin primes, the origin of sexy primes and their classes, the structure of the chain prime numbers, the determination in the order of the set of prime numbers less than a given integer, the Mersenne number, the Fermat number, these problems were considered by mathematicians as an impenetrable domain or even a myth which has persisted for over 2000 years.

This work has shed light on the world of prime numbers by providing solutions for each of these eight problems cited above.

It's all about numbers, it's all about measurement. Said Severinius BOECE (480-524, Rome) “Everything was created by numbers which were the exemplary model in the mind of the creator”, the understanding of prime numbers can facilitate the understanding of other sciences

Three mathematical conjectures, namely twin primes, cousin primes and sexy primes, have been solved in this book entitled The End of the Prime Number Mystery. We have also shown in the book the class of a prime number, we have shown the structure of the chain of prime numbers, we have established the set of prime numbers less than a given integer, we have given a method of preliminary identification of a prime number, we have shown the origin of Mersenne's number and Fermat's number, we have established two pairs of equations which are objects of mathematical conjecture.

This work is made available to the world scientific committee so that humanity can fully understand prime numbers.

Content

Exploration and Classification of Prime Numbers: A Systematic Approach

Mady Ndiaye

Exploration and Classification of Prime Numbers: A Systematic Approach, 15 July 2024, Page 1-44
https://doi.org/10.9734/bpi/mono/978-81-976932-5-0

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.