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The book of the discovery of prime numbers formula and its results & other top researches is now ready to buy

by Seyyed Mohammad Reza Hashemi Moosavi

The book of the discovery of prime numbers formula and its results & other top researches is now ready to buy

   

 

 

 

 

 

 

 

 

 

 

 

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We have the honor to say happy new year of 2022 to the people of the world, especially mathematics lovers. Behalf all the employees of publications and company also HM Institute.

 Professor Seyyed Mohammadreza Hashemi Moosavi , the designing team and the manager of the Hamsa-HM Company with cooperation of Meraje Ghalam Publications under the management in chief of Seyyed Alireza Hashemi Moosavi started its work from 2003 until now. It means that I gave a condition as a job those days but those days people didn't think that internet grows so fast that Alexa that was starting its beginning years of Establishment and there was no name of neither of us now both of us big enough. Of course I don't know exactly why they (Alexa) gave up so fast, because I believe we don't have an SEO first bringer and beginner of some thing important that I want to say wow Alexa did great its work. What a great prediction of future they had in that they that started this big and very important project as soon as the internet started to be popular between the countries and it was a new big wave of the revolution. Administration decided such an absolutely shakable decision indeed and I would respect they point of view to close the project of Alexa in the informed way and day if you didn't know that, of course I know that Its so Important for the specialists that for sure I am just telling my opinion actually.

In the upper place of the home page of Alexa's Webpage there is a message about their decision about the future of they very good project and close it until March 2022 as they Informed already in a left message. Doesn't matter for us what happened, I believed in the main genius brain of the Alexa agency that suddenly people found themselves in Alexa ranking for the first time in history , I remember like this. About 2003 There was a fact that I do remember just one first name in ranking like ourselves in the past.  We exactly made a new concept that in 2003 and 2004 there wasn't such a bold field and at last because of Hardy that had said that there is no formula for prime numbers then so people it was like that all believed in Hardy's words except some insister. Hardy was so wrong now we know. He thought that these numbers with such a beautiful place in the general arrangement of integer numbers they have, Is it possible that doesn't follow a pattern?!

My answer would be exactly for any kind of scientific event in life is that there is a pattern, formula or rule . I don't know what do you want to call it. Nowadays most of people know that very first importance of prime numbers is for communications and cryptography. We have the honor to be The First Reference of Prime Numbers Formula that about the 2003 we started our Website about the great discovery of the Professor in the open source way for the people of the world to be so fast inspirable for them to first of all use freely the benefits of huge applications of this revolutionary research victory and take the new Ideas and methods for themselves in other fields of science that I would say that there is nothing like prime numbers formula existence is so important.

Most of the forums and communities remember those days, because you can just by one googling find so many of them with the archives that is stored as websites documents and evidences are more than that you can ignore but it sounds there is some people don't like to notice and this is just far away the clear evidences and documents we have that Harvard sent the invitation of professor Safari (The one that made google Safari) to Professor Seyyed Mohammadreza Hashemi Moosavi to visit Harvard for some more explanations about the other aspects of the main idea and some more information about the real formula. I have to tell you that first those days we started to aware 121 numbers of  ISI journal of mathematics in so many countries around the world that at least one person know the truth and there was no way but mentioning about the real that ukessay still has a clear document that simply use the main fact in background and in the concept of the article say that Professor with his discovery in the year of 2003 proved that impossible can still be possible and his opinion in the Article was that if you have some doubt about Impossible maybe there was a chance we should have the point of view of doubt in philosophy of the life about that fact.

 About the discovery of prime numbers formula and its results, because there was speaking about the honor of being the first one and  a 7 million Dollar prize for 7 unsolvable millennium prize existed that clay institute started to offer for some problems that Professor Solved it as the first one. The prime numbers formula that honestly I shared at the first was the old version that I knew that is not important. Its so odd that they couldn't understand from my codes of programming and my beautiful new method about symmetric and central HM Magic Squares and the big applications that just those ones that like some chapters of the The Discovery Of Prime Numbers Formula book and its Results that now we have the permission to sell the PDF files of the book. For the first time the old versions of the Discovery that the governments don't let you spread and develop the time came to we have in 3 shift of working hours in 24 hour a day about 66 employees to be at your service and the Publications decided for the security its sale is just with Ethereum Wallet and we don't have other way. You just pay and receive your E-Book of the title and you will see for the first time the main idea that made such a big revolution in the number theory. That unfortunately didn't happened because of some hands behind the seen. Actually, they wanted and want to ignore the existence of us, so many websites like wikipedia. When in google website search engine you began to start the search about prime numbers formula because there was no such a concept until the year 2003.

There is an Address of Digital Wallet that only we receive in Ethereum only and there is a price that our publications in sponsorship of Meraje Ghalam let us

to know is 0.2 Ethereum that in US Dollar is about 450$ .

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  Pay me via Trust Wallet: https://link.trustwallet.com/send?coin=60&address=0x9a499a73BadF7f5157724Fb6A0d6e22a38130e37&amount=0.

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Just now take your QR-Code scanner to guide you to use the auto payment that is fixed in 0.2  Ethereum  and don't forget just use Ethereum.

So now you have two option that the first is QR-Code that like the link is a request for payment that after using that it sends you for a transaction.

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This was the last step and when you push the send bottom then the process is done. Now After payment you will receive the successful message.

sent information in your wallet only an screen shot of that confirmation is enough to send via the Email. As soon as its possible the Sell Office will send you your PDF file of the book.

 Professor Seyyed Mohammadreza Hashemi Moosavi as the publications of Meraje Ghalam is our sponsor www.komhm.com and its a

version of www.primenumbersformula.com in another language and the temporary website in position of the publications. You can see some of the books that

 are waiting for the last review and soon will be ready for you to buy and use the new revolutionary methods and the golden  equations like the Real prime 

Numbers Formula.

 As I told you in my explanations the formula that we freely developed was so useful for researchers and we wanted the world to know and use method of HM

but for sure we couldn't just gave the formula without the proofs that clearly and beautifully for the first time you will so many new knowledge that you have not seen

in your life specially in number theory. Some people believe that just this big revolution just appeared or some people say that it is some thing that is found by

X or Y.

None of these is correct  that you will figure out when you just read the PDF of the E-Book that sell office team after you sent just an screen of the successful payment absolutely you have some information that helps us to check with a document that shows your payment information. Our team rapidly will check your claim and in 30 minutes you will receive the PDF of the E-Book .

To start your buying send the requested payment to the Address of Wallet just by scanning the QR-Code and then use the QR-Code of below to send email. It contains an Email

Address that goes to the Sell-Office and don't forget to use the request payment to correctly send your Ethereum to the right address and attach the successful transaction and payment document as an screen shot or whatever else that t you can submit to show the sell-office your trueness of your claim and send you your file as soon as its possible.

In Emergency you can send email to hamsa.hm.1400@gmail.com or just use the Whatsapp with the number of : +989300521913 Seyyed Alireza Hashemi Moosavi

So in this case I will directly in a short time troubleshoot it.

                 

        This was for your relief that at last myself will be in the circle of selling team and finally after doing every step.

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you can freely download pdf file of chapter 1 . Book of the discovery of prime numbers formula and its results

you can freely download pdf file of chapter 2 . Book of the discovery of prime numbers formula and its results

you can freely download pdf file of chapter 3 . Book of the discovery of prime numbers formula and its results

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Freely download prime numbers formula software package by Seyyed Alireza Hashemi Moosavi

 

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The book of the discovery of prime numbers formula and its results

Seyyed Mohammad Reza Hashemi Moosavi

 

 

Table of contents of the book

The discovery of prime numbers formula and its results

                                "Table of contents"

   Contents

Preface of author

1. A brief of view of number theory           

1.1   Number theory in ancient time................................................ 12

1.2   What is number theory?........................................................... 14

1.3   Prime numbers......................................................................... 20

1.4   The fundamental theorem and some of its applications.......…………………... 22

1.5   Sieve of Eratosthense.............................................................. 26

1.6   Periodic sieve for small numbers............................................. 27

1.7   The infinity of prime numbers................................................. 29

1.8   Functions,  and .............................................................. 30

1.9   Perfect numbers....................................................................... 33

1.10 Bertrand’s principle and theorems of Chebyshev, Dirichlet and Poisson..............................................................................................35

1.11 Lagrange’s theorem..................................................................................................................................................................................    38

 

2. On the history of forming prime numbers tables and determining the smallest divisor of composite numbers ...........................   .........  42

2.1 Famous tables of prime numbers and divisors of composite numbers   ............................................................................................................    43

2.2 Calculation of tables...................................................................................................................................................................................................... 44

2.3 Stochastic’s theorem...................................................................................................................................................................................................  45 

2.4 Another research on stochastic theorem....................................................................................................................................................................  54

2.5 Table of divisors of Burkhard......................................................................................................................................................................................... 55

 

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

 progressions and successive cycles  ....................................................................................................................................................................58

3.1 "H.M" matrix table (zero and one) for recognizing prime numbers and devisors of composite numbers ...............................................59

3.2 "H.M" Loop table for recognizing prime numbers and divisors of composite numbers………………………………………………     60

3.3 "H.M" Loop-cycle table for recognizing prime numbers and divisors of composite numbers  ………………………………………… 63

 

4. On the history of the problem of recognizing prime numbers by two sided theorem

in particular Wilson’s theorem and its consequences   ………………………………………………...............................................………   66

 

4.1 Wilson’s theorem ...................................................................................................................................................................................................... 67

4.2 Remarks concerning Wilson’s theorem and its converse and corollaries.............................................................................................     69

4.3 Corollaries of Wilson’s theorem...................................................................................................................................................................... 70

4.4 Some of if theorems for recognizing prime numbers ................................................................................................................................... 73

4.5 Factorization of composite numbers............................................................................................................................................................... 77

5. Decisive solution to the problem of recognizing prime numbers by a formula concerning recognizing of numbers "" ............................................79

5.1 Determination of the formula for the characteristic function of numbers ........................................................................................................................................... 80

5.2 Formula for surjective characteristic function........................................................................................................................................................................................ 83

 

6. On the history of the problem of searching for finding generating function of prime numbers " ................................................................................... 85

6.1 A summery of the history of "2000" years old attempts for finding a formula for prime numbers...................................................................................................   86    

6.2  Mills’s theorem.............................................................................. 87

6.3  Kuipers’s theorem......................................................................... 87

6.4  Niven’s theorem............................................................................. 88

6.5  Formulas of generating prime numbers................................... . 88

6.6  Generalized Mills’s theorem..................................................   .... 92  

6.7  Investigation into polynomials...................................................     94

6.8  A formula presenting for generating prime numbers by Wilson’s theorem…………………………………………………………………….97

 

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

the surjective generating function of prime numbers   ………………………………………………………………………………………………      99

7.1 Determination of the formula for the surjective generating function of prime numbers  …………………………………………………………  100

7.2 Domain and range of the surjective generating function of prime numbers……………………………………………………………………  …100

 

8. On the history of the problem of determining the number of prime  and its related functions "" and "………………………… 103

8.1 An introduction to the function ""and "li"............................  104

8.2 Prime numbers theorem..........................................................107

8.3 The function "li" or "the logarithmic integral"......................... 109

8.4 Missal's formula for "".................................................... 110

 

9. Decisive solution to the problem of determining of the precise number of "" primes by characteristic function ""…………………   113

9.1 Determining "" by ""......................………………………………………………………………………………………………............................. 114

9.2 Comparing the precise formula for ""with Missal's formula …………………………………………………………………………………………… 116

 

10. On the history of determining "k-th" prime number by bounds for "" (determining lower and upper bounds for "")………………………… 118

10.1 Determining the bounds for "" (the "k-th" term of the sequence of prime numbers) ……………………………………………………………………   119

10.2 Bounds for "" from below and above ............................... 120

10.3 Bonze's theorem.................................................................... 121

10.4 Theorems concerning consecutive prime numbers ........... 121

10.5 Theorems of Chebyshev........................................................ 122

10.6 Theorems of Ishikawa............................................................ 123

 

11. Decisive solution to determining "k-th" prime number by determining function concerning the number of prime in a precise manner……………… 125

11.1 Determination of "" in a precise manner .................................................................................  ..................................................126

11.2 Other formulas for determining "" in a precise manner.............................................................................................................. 127

 

12. On the history of attempts for solving Riemann zeta equation  "" and the low of rarity of prime numbers …………………………… 130

12.1 Riemann's zeta function and its celebrated equation ""………………………………………………………………………………………     131

12.2 An introductory method for finding a fundamental formula  for ""  …………………………………………………………………………………  132

12.3 Statistical investigation into the fundamental formula for "" ...………………………………………………………………………………………140

12.4 Separating intervals of prime numbers.......................……………………………………………………………………………………………………  140

 

13. Decisive solution to Riemann zeta equation () by the determining function concerning the precise number of primes () ………143

13.1 Riemann’s zeta function ()..........................................………………………………………………………………………………………………………144

13.2 Decisive solution to Riemann's zeta equation ()  Millennium prize problem……………………………………………………………………   145

14. On the history of searching for famous prime numbers and the factorizations of these numbers ()……………………………………    147

14.1 Some of famous numbers...................................................... 148

14.2 Fermat’s numbers................................................................... 149

14.3 Special problems and Fermat’s numbers...........................  154

14.4 Another proof for Euclid’s theorem......................................   157

14.5 Speed of the growth of Fermat’s numbers............................ 157

14.6 Fermat’s numbers and the problem of inscribing regular polygons inside a circle ………………………………………………………… 158

14.7   Refutation of Fermat’s assertion and factorization of Fermat’s numbers……………………………………………………………………159

14.8   Mersenne’s numbers............................................................... 159

14.9   Problems concerning Mersenne’s numbers.......................... 160

14.10 Perfect, imperfect and redundant numbers............................ 161

14.11 Historical remarks concerning (even) perfect numbers and Mersenne’s numbers………………………………………………………        64

14.12 Role of computers in searching large prime numbers......………………………………………………………………………………………166

14.13 Odd perfect numbers............................................………………………………………………………………………………………..........…  168

14.14 Special problems concerning perfect numbers............…………………………………………………………………………………………. 168

14.15 Problems on distinguishing Mersenne’s prime numbers and Fermat’s numbers …………………………………………………………    170

14.16 Problems concerning Fermat (), Mersenne (), perfect and redundant numbers    ……………………………………………………   174

 

15. Definition of the sets of Fermat, Mersenne, perfect prime numbers by the prime numbers formula  …………………………… … 177

15.1 Some general facts concerning Fermat’s numbers ()......……………………………………………………………………………………... 178

15.2 Definition of the set of Fermat’s prime numbers by the prime numbers formula     ............................................................................................   178

15.3 Some general facts about Mersenne’s numbers and even perfect numbers and the relation between them................................................... 179

15.4 Definition of the sets of Mersenne, even perfect prime numbers by the prime numbers formula   ..................................................................... 179

 

16. On the history of attempts for proving Goldbach and Hardy  conjectures..........................................................................................................................181

16.1 Gold Bach and Hardy’s conjectures......................................................................................................................................................................................... 182

16.2 Gold Bach's conjecture and other open problems related to it ............................................................................................................................................  182

16.3 Some unsolved problems and other conjectures concerning  prime numbers  .................................................................................................................... 184

16.4 Applied investigations into Goldbach and Hardy conjectures .............................................................................................................................. ...................186

16.5 Theoretical investigation into Goldbach conjecture................................................................................................................................................................... 186

 

17. On the history of attempts for proving the conjecture of existence of infinity many twin prime numbers..................................................188

17.1 Twin prime numbers ............................................................. 189

17.2 Clement’s theorem ................................................................ 190

17.3 Approaching to the solution of problem of infinity many twin prime numbers......................................................................................  ....... 190

17.4 The distances of prime numbers........................................................................................................................................................................ 190

17.5 Definitions and notes…………………………............................................................................................................................……………….191

17.6 Problems concerning twin prime numbers......................................................................................................................................................... 193

 

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  ............................................................................................................................        194          

18.1 Generation of twin prime numbers ...............................................................................................................................................................  ........ 195

18.2 There is infinity many twin prime numbers.............................................................................................................................................................. 199

18.3 Set of prime twin pairs………………………………………...........................................................................................................................…….201

 

19. On the history of attempts for proving Fermat’s last theorem and the fundamental role of prime numbers (regular) and its properties      

 leading to solving Diophantine equation  ........................................................................................................................................................... 202                 

19.1 Diophantine equations................................................................................................................................................................................................ . 203

19.2 An introduction to the chronology of Fermat’s last theorem ......................................................................................................................................203

19.3 Chronology of Fermat’s last theorem........................................................................................................................................................................ . 204

19.4 Sophie Germain’s theorem...........................................................................................................................................................................................218

19.5 Fermat’s last theorem for exponent "4".....................................................................................................................................................................   221

19.6 Fermat’s last theorem for exponent "3"......................................................................................................................................................................  225

 

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 equations
............................................................................   ...229

20.1 Investigation into extension Fermat’s last theorem .......................................................................................................................... .. 230

20.2. Primitive, Algebraic and geometric methods....................................................................................................................................................... ..  231

20.3 An indirect proof of Fermat’s last theorem (elliptic curves)....................................................................................................................................  234

20.4 Taniyama- Shimura – Weil conjecture and Fermat's last theorem ..................................................................................................................... . .250

20.5 Frey-Serre-Ribet theorem………………………………............................................................................................................................…………251

20.6 Wiles and Taylor-Wiles theorem …………………….............................................................................................................................................…251

20.7 Latest achievements and fundamental results concerning Fermat’s last theorem and its extension (H.M)...................................................... 252

20.8 Reducibility law (H.M)................................................................................................................................................................................................   256

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

         …………………………………….......................................................................................................................................... 258        

20.10 Solving Diophantine equations having non-similar exponents (multi-equalities) (H.M)…….....……………………….....................….……..267

20.11 Finding an answer for extension of Fermat’s last theorem using the theorems related to prime numbers (H.M) ….........................……….269

              

20.12 Determining a general answer for equation (H.M)……...........................................................................................................................……… 270

               ,

 20.13 Determining a general answer for equation (H.M)……........................................................................................................................................272

              

20.14 Determining a general answer for equation (H.M)…………...........................................................................................................................……273

             (the Fermat-catalan and the Beal conjectures "")

          

20.15 Determining a general series of answer for Diophantine equations with arbitrary degree by using Wilson’s, Fermat’s and Euler’s theorems and

 the role of prime numbers formula in arising of Algebraic identities (H.M).................................................................................................................... 275

                

21. The newest of methods of solving and calculating    

    Appendixes (I) ........................................................................................................................................................................................................................... 287

21.1 Solving congruence and Diophantine equations by  "H.M" table ()...........................................................................................................…...288

21.2 Solving linear Diophantine equations by "H.M" table

        ……………………………....................................................................................................................................………………..294

21.3 Solving "n-th" degree Diophantine equation by "H.M" table …………………………………………...............................…………..298

21.4 A new and fast method for calculating of determinant ("H.M" method).......................................................................................................... 302

21.5 Definition of regular and irregular prime numbers by "H.M" determinant............................................................................................................... 309

21.6 New method of calculation of sum of "k-th" power of the first "n" natural numbers

 by "H.M" determinant (expressing "" by a determinant)…………………………………..............................................................…………………...314    

21.7 Determining the number of roots of perfect cubic degree equation directly by "H.M" method............................................................................   316

 

21.8 Proof of a new and applied "H.M" theorem (Concerning the factorization of composite numbers)..................................................................... 318

 

22. The abstract of formulas and their software programs

Appendixes (II)  ...................................................................................................................................................................................................................... 320

22.1 The abstract of the distinction formula of the prime numbers...................................................................................................................................  321

22.2 The distinction program of the prime numbers.................................................................................................................................................. 322

22.3 The abstract of the formula of the prime numbers generator      .............................................................................. ................................. .....  323

22.4. The final formula of the prime numbers generator............................................................................................... ......................................   ......323

  22.5 The program of the prime numbers generator............................................................................................................................... ....................325

22.6 The abstract of the formula of the determining of the "k-th" prime number .......................................................................................................   327

22.7 A program for determining the prime number "k-th"......................................................................................................................... ................... .328

22.8 The abstract of Riemann’s zeta equation solution ......................................................................................................................................  . 329

22.9 A Program for determining of the number of the prime numbers smaller than or equal any arbitrary number "p" exactly.................  330

22.10 The abstract of the definition of the prime numbers set by using  the surjective generating function of the prime numbers (IP)....................   . 331

22.11 A program for defining the prime numbers set (IP)............................................................................................................................................  ...... 332

22.12 The abstract of the definition of the Mersenne’s prime numbers set by using the prime numbers generator............333

22.13 A program for determining the Mersenne’s prime numbers of M-digits (M: Arbitrary number)............................................................................ 334

22.14 The New Mersenne’s prime number as "42nd" known Mersenne prime found (February 2005) ........................................................................337

22.15 The determining of generating function of the prime numbers greater than the greatest prime number by prime numbers formula.............................................................................................................................................................................................................................  338

 

 


 

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You can freely download prime numbers formula software. Open source code of Seyyed Alireza Hashemi Moosavi's program is in follow that is based on H.M formula of prime numbers that was discovered in the year of 2003  Prof. Seyyed Mohammad Reza Hashemi Moosavi.

 Note : You are just permitted to use the subject with mentioning the reference address of the 

Site : www.primenumbersformula.com

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Take a look at new photo gallery

Note : This formula is one of the on-to generating functions for the prime   numbers that for every natural "m" it generates all the prime numbers (3,5,7,2,11,13,2,17,19, ...)

The presented "H.M"  functions by Discoverer (Prof. Seyyed Mohammad Reza Hashemi Moosavi) are 6 numbers that 4 functions are by Wilson's theorem and one of them by Euler's function( ) and one of them by functions and functions are discovered by discoverer (Prof.S.M.R.Hashemi Moosavi). The software of this function is produced.

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Note :  In Year of 2007 (AAAS) " National Association Of Academies Of Science " (USA) Awarded an A++ = Excellent grade to prime numbers formula and its results by prof.S.M.R.Hashemi Moosavi.  

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Note :  The discovery of prime numbers formula and its results has been published under an article in journal of "Roshd of Borhan " , associated with Ministry of Education.

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 More explain about discovery of prime numbers formula

 Infinity proof of prime numbers was propound 300 years before the Christian era by Euclid and since that time great mathematician like Euler try to discover a formula for production of prime numbers.

Euler could define a quadratic function which give prime numbers for forty prime number which are uninterrupted and also Fermat presented a formula to obtain prime numbers and later, it breached by Euler for n = 5.

Many of other mathematicians achieved to violating and especially formula and finally they found that discovery of prime numbers formula is impossible and this problem will be unsolvable.

In fact this discovery means that one of complicated and unsolvable mathematics problem was solved and this discovery give this fact to man that earthy human can solve other unsolvable problems with research and effort.

I have worked about this problem around 20 years and I found this fact that I can't comeback from this path which I came and I promised that search about this un solvable problem till end of my life even if I couldn't achieve the final solution.

Of course my research had result with patronage under god and trust in god and I discovered the formula of prime numbers.

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How is the usage of this formula in mathematics  and other sciences?

 A result for discovery of prime numbers formula is the solution of Riemann Zeta equation which is on of seven universal unsolvable problems in mathematics millennium and it's solution need to gain the number determination equation of prime number for any desirable number n carefully (with prime numbers formula).

Another result is determination of Kth desirable prime number and other usages are definition of prime number set, proof of infinity of prime twin pairs, considering of the guesses of Goldbuch and Hardy, gaining the generator formula of Mersenne prime numbers and also very unknown and big prime numbers and other problems related to prime numbers.

But the basic and cardinal usage of this formula is in coding and decoding that usually use from very big prime numbers for this and before it is necessary to gain them with complicated mathematics methods. But with presenting of this formula, definition of coding and decoding system became easy and I invent a system for coding with this formula that I presented this system inventions registration organization.

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After Euclid’s theory about infinite prime numbers in 300 B.C Most of the mathematicians and other researchers have been curious to find a formula which could generates prime numbers. After many years later, some mathematicians like Euler and Fermat presented some formulas to generate prime numbers limitedly.

Great mathematicians like Hardy and Courant and many other researchers officially announced that such a formula can’t be found and in follow to prove their wrong idea they started to publish some Algebraic theorems in their books.

Meanwhile, Niven and Mills in relation to prime numbers function proved the above theorem. But their parameters have never been determined.

Furthermore, determining the number of prime numbers was very important problem. So Gauss and other mathematicians started to set some tables for them.

We knew that there is no exact formula to determine the number of prime numbers exactly. This problem is known as Zeta Riemann equation which was one of the seven known unsolvable problems of the world that after my discovery on 5th August 2003, one of them is no more unsolvable with the prime numbers formula accurately you can absolutely generate all prime numbers to the nth one.

Its consequent generate of prime numbers formula resulted in defining the set of prime numbers and so many other unbelievable results until now like breaking the code of RSA and AES by the use of prime numbers formula and other sets like Mersenne prime, perfect numbers and so many important sets and results just related to the field of number theory and basic sciences.

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  • Discovery of prime numbers formula by Prof. Seyyed Mohammadreza Hashemi Moosavi caused so many results in basic sciences that we will mention a little part in follow:

  • 1.         Distinction of prime numbers.

  • 2.       Defining a formula for generating prime numbers.

  • 3.       Definition of prime numbers set by using the generating function of prime numbers.

  • 4.       Defining a formula to generate the Mersenne prime numbers.

  • 5.       Determination of Nth prime number.

  • 6.       Solving Riemann Zeta equation by using the determination of the number of prime number less than or equal to arbitrary number N exactly.

  • 7.       The proof of guesses of Gold Buch and Hardy.

  • 8.       The proof of infinity of the prime twin couples.

  • 9.       Determining a general series of answer for Diophantine equations.

  • 10.   This formula has so many unknown applications in Cryptography, generating Titan Mersenne prime numbers and other sciences like solving  NP.

 

 

 

 

 

 

 

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