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08/26/20

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         Seyyed Mohammad Reza Hashemi Moosavi                                                          

                                                                       Discoverer of prime numbers formula    

 

         Introduction :

  I am Seyyed Mohammad Reza Hashemi Moosavi and university professor that I chosen as a superior investigator in superiors and initiators festival in 1383. My academic course is telecommunication electric engineering and I received specialized doctorate of Education (PhD) from Boston university of America and doctorate of mathematics (PhD) from Spain.

              researching works :

  I have started my researches in mathematics field when I was fourteen. My first research was a flash that one of my mathematics teachers in guidance school caused it. He pronounced a method of mental multiplication of numbers. Impetus of mental multiplication occupied my mind to research for several years. Till in first year of high school, I could obtain a mental multiplication method for M figures and N figures and it was my first success in research works. My second research which lasted around two years was obtain the method of algebraic and geometric solution in cubic equation that I obtain in fourth year in high school and published in 22nd copy of mathematics teaching development magazine from research and lessons programmer organization. After it I researched seriously. For example calculation of K-th strength for n prime number that I express Sk a determinant which it doesn't need to Bernoulli coefficients or analysis methods. This point published in 16th copy of mathematics teaching development magazine too and then in 1994 it published in spectrum (the university Sheffield) in England.

I obtain the calculation of ellipse circumference which has many usages in calculation of integral function and ellipsoid integral in analysis in a perfectly analytic method and it will publish in spectrum magazine. I performed another research like congruence equation solution in table method that it gives answer of every congruence equation with optional coefficient in the shortest time which is possible.

My other research was presented a new method with a highest race of calculation for N*N determinant and it published in spectrum magazine in 2003.It is necessary to mention this point that all of these research became pedestal for my next research like obtaining the prime number formula.

My other researches are integral expansion to series and calculation of integrals which have N-th power and express in a returning method. These articles published in ''Acquaintance with mathematics '' too and also my other researches that published in different copy of this magazine.

My another important and basic researches is solution of fluid equation in N-th degree that has a great usage in engineering sciences and researching center .of course I performed a lot of researches in algebra, analysis , number theory field and other mathematics branches.

My books

   My books

 My writings are more than 17 copies that all of them had published and of course another   books (more than 19 copy) that I translated or edited scientifically.

 I have written other books in university and Olympia levels and one of the master pieces of mathematics works that was collected with collaboration of other mathematics cooperators group in "school publication" is mathematics dictionary.

 also more than 34 specialized articles printed in out side and in side creditable magazines. Lots of my researchable investigational books like "Essentials of Coding and Decoding" and new researches in mathematics and other titles also are ready to publish.

                                                                                                                                                                           


Table of contents of the book

 

The discovery of prime numbers formula and its results

 

  "Table of contents "

   Preface of author

    1. A brief of view of number theory

1.1   Number theory in ancient time

1.2   What is number theory?

1.3   Prime numbers

1.4   The fundamental theorem and some of its applications

1.5   Sieve of Eratosthense

1.6   Periodic sieve for small numbers

1.7   The infinity of prime numbers

1.8   Functions,  and

1.9    Perfect numbers

1.10 Bertrandís principle and theorems of Chebyshev, Dirichlet and Poisson

1.11 Lagrangeís theorem

2. On the history of forming prime numbers tables and determining the smallest divisor of composite numbers

2.1 Famous tables of prime numbers and divisors of composite numbers.

2.2 Calculation of tables

2.3 Stochasticís theorem

2.4 Another research on stochastic theorem

2.5 Tables of divisors

2.6 Burkhardís tables

 3. Decisive solution to the problem of forming of tables concerning divisors of composite numbers by regular loops in                                                              arithmetic progressions and successive cycles

3.1 "H.M" Matrix table (zero and one) for recognizing prime numbers and devisors of composite numbers           

3.2 "H.M" Loop table for recognizing prime numbers and divisors of composite numbers 

3.3 "H.M" Loop-cycle table for recognizing prime numbers and divisors of composite numbers    

       4. On the history of the problem of recognizing prime numbers by two sided theorem in particular Wilsonís theorem and its consequences

4.1 Wilsonís theorem

4.2 Remarks concerning Wilsonís theorem and its converse and corollaries         

4.3 Corollaries of Wilsonís theorem

4.4 Some of if theorems for recognizing prime numbers

4.5 Factorization of composite numbers

 5. Decisive solution to the problem of recognizing prime numbers by a formula concerning recognizing of numbers ""

5.1 Determination of the formula for the characteristic function of numbers           

5.2 Formula for surjective characteristic function

        6. On the history of the problem of searching for finding generating function of prime numbers ""

6.1 A summery of the history of 2000 years old attempts for finding a formula for prime numbers 

6.2  Mill's theorem

6.3  Kuiperís theorem

6.4  Nivenís theorem

6.5  Formulas generating prime numbers

6.6  Generalized Mills theorem

6.7  Investigation into polynomials

6.8 A formula presenting for generating of prime numbers by Wilsonís theorem    

 7. Decisive solution to the problem of finding the generator of prime numbers via discovering the surjective generating function of prime numbers

7.1 Determination of the formula for the surjective generating function of prime numbers   

7.2 Domain and range of the surjective generating function of prime numbers

 8. On the history of the problem of determining the number of prime and its related functions "" and ""

8.1 An introduction to the function ""and "li

8.2 Prime numbers theorem

8.3 The function "li" or "the logarithmic integral"

8.4 Meisselís formula for ""

 9. Decisive solution to the problem of determining of the precise number of  "" primes by characteristic function ""

9.1 Determining "" by ""

9.2 Comparing the precise formula for ""with Meisselís formula

       10. On the history of determining "k-th" prime number by bounds for "" (determining lower and upper bounds for "")

10.1 Determining the bounds for "" (the k-th term of the sequence of prime numbers)   

10.2 Bounds for "" from below and above

10.3 Bonseís theorem

10.4 Theorems concerning consecutive prime numbers

10.5 Theorems of Chebyshev

10.6 Theorems of Ishikawa

 11. Decisive solution to determining "k-th" prime number by determining function concerning the number of primes in a precise manner

11.1 Determination of  "" in a precise manner

11.2 Other formulas for determining "" in a precise manner

 12. On the history of attempts for solving Riemann zeta equation and the low of rarity of prime numbers

12.1 Riemann zeta function and its celebrated equation ""

12.2 An introductory method for finding a fundamental formula for ""

12.3 Statistical investigation into the fundamental formula for ""

12.4 Separating intervals of prime numbers

         13. Decisive solution to Riemann zeta equation

() by the determining function concerning the precise number of primes ()

13.1 Riemann zeta function ()

13.2 Decisive solution to Riemann zeta equation ()

 14. On the history of searching for famous prime numbers and the factorizations of these numbers ()

14.1 Some of famous numbers

14.2 Fermatís numbers

14.3 Special problems and Fermatís numbers

14.4 Another proof for Euclidís theorem

14.5 Speed of the growth of Fermatís numbers

14.6 Fermatís numbers and the problem of inscribing regular polygons inside a circle       

14.7   Refutation of Fermatís assertion and factorization of Fermatís numbers

14.8   Mersenneís numbers

14.9   Problems concerning Mersenneís numbers

14.10 Perfect, imperfect and redundant numbers

14.11 Historical remarks concerning (even) perfect numbers and Mersenneís numbers    

14.12 Role of computers in searching large prime numbers

14.13 Odd perfect numbers

14.14 Special problems concerning perfect numbers

14.15 Problems on distinguishing Mersenneís prime numbers and Fermatís numbers      

14.16 Problems concerning Fermat (), Mersenne (), perfect and  redundant numbers         

 15. Definition of the sets of Fermat, Mersenne, perfect prime numbers by the prime numbers formula

15.1 Some general facts concerning Fermatís numbers ()

15.2 Definition of the set of Fermatís prime numbers by the prime numberís formula        

15.3 Some general facts about Mersenneís numbers and even perfect numbers and the relation between them      

15.4 Definition of the sets of Mersenne, even perfect prime numbers by the prime numbers formula          

        16. On the history of attempts for proving Goldbach and Hardy  conjectures

16.1 Goldbach and Hardy conjectures

16.2 Goldbach conjecture and other open problems related to it

16.3 Some unsolved problems and other conjectures concerning prime numbers  

16.4 Applied investigations into Goldbach and Hardy conjectures

16.5 Theoretical investigation into Goldbach conjecture

 17. On the history of attempts for proving the conjecture of existence of infinity many twin prime numbers

17.1 Twin prime numbers

17.2 Clementís theorem

17.3 Approaching to the solution of infinity many twin prime numbers

17.4 The distances of prime numbers

17.5 Problems concerning twin prime numbers

        18. Decisive solution to the problem of infinity many twin prime numbers and method of generating them and definition of twin prime numbers set  by                   twin prime numbers formula 

18.1 Generation of twin prime numbers

18.2 There is infinity many twin prime numbers

 19. On the history of attempts for proving Fermatís last theorem and the fundamental role of prime numbers (regular) and its properties leading to solving Diophantine equation  

19.1 Diophantine equations

19.2. An introduction to the Chronology of Fermatís theorem

19.3. Chronology of Fermatís theorem

19.4. Fermatís theorem, for exponent 4

19.5. Fermatís theorem, for exponent 3

 20. Fundamental role of prime numbers and its properties in a complete investigation into Diophantine equations in the sense of existence or
non-existent solution and presenting a general solution for the Diophantine equation

20.1 Investigation into extension Fermatís theorem

20.2. Primitive, Algebraic and geometric methods

20.3 An indirect proof of Fermatís theorem (elliptic curves)

20.4 Taniyama- Shimura Ė Weil conjecture and Fermat last theorem

20.5 Theorems of Wiles and Taylor-Wiles

20.6 Latest achievements and fundamental results concerning Fermatís last theorem and its extension (H.M)        

20.7 Reducibility law (H.M)

20.8 Studying Diophantine equation of n-th order (similar exponents) (H.M)

              

20.9 Solving Diophantine equations having non-similar exponents     (multi-equalities) (H.M)

20.10 Finding an answer for extension of Fermatís last theorem using the theorems related to prime numbers        

20.11 Determining a general answer for equation

20.12 Determining a general answer for equation

20.13 Determining a general answer for equation

         

20.14 Determining a general answer for equation (H.M)

20.15.Determining a general answer for equation (H.M)

20.16 Determining a general answer

         21. The newest of methods of solving and calculation

                                   Appendixes (I)

21.1 Solving congruence and Diophantine equations

by "H.M" table  ()

21.2 Solving Diophantine equation of order in by "H.M" table

21.3 A new and fast method for calculating determinant ("H.M" method)    

21.4 Definition of regular and ir-regular prime numbers by "H.M" determinant.     

21.5 New method of calculation of sum of  "k-th" power of the first "n" natural numbers by "H.M" determinant (Expressing "" by a determinant)

21.6 Determining the number of roots of perfect cubic degree equation directly by "H.M" method

21.7 Proof of a new and applied "H.M" theorem (Concerning the factorization of composite numbers)     

 22. The abstract of formulas and their software programs

                                    Appendixes (II)

22.1 The abstract of the formula of the formula of the function distinction of the prime numbers.     

22.2 The program for distinction of the prime numbers

22.3 The abstract of the formula of the prime numbers generator

22.4. The final formula of the prime numbers generator

22.5 The program of the prime numbers generator

List of my books

           here is the list of ISBN of some of my books below :

  • Dictionary mathematics - 606 pages - ISBN : 964-436-941-6

  • Basic mathematics - 348 pages - ISBN : 964-310-016-2

  • Calculus - Editor - 311 pages - ISBN : 964-6214-42-8

  • Calculus - Editor - 357 pages - ISBN : 964-6214-41-x

  • Calculus - pages 347 - ISBN : 964-91766-6-7

  • Calculus - pages 447 - 3rd impression - ISBN : 964-353-720-x

  • Power and radical - 188 pages - 6th impression - ISBN : 964-353-852-4

  • vectors - 150 pages - 4th impression - ISBN : 964-353-880-x

  • Limit - 148 pages - 12th impression - ISBN : 964-385-003-x

  • Defines of the domain and range functions - 135 pages - 13th impression -ISBN : 964-385-114-1                         

  • Olympiad mathematics - Editor - 208 pages - ISBN : 964-353-021-3

  • The problems mathematics - 175 pages - ISBN : 964-6150-25-x

 

        

 

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