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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 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.
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 Bertrand’s principle and theorems of
Chebyshev, Dirichlet and Poisson
1.11 Lagrange’s 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 Stochastic’s theorem
2.4 Another research on stochastic theorem
2.5 Tables of divisors
2.6 Burkhard’s 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 Wilson’s theorem and its
consequences
4.1 Wilson’s theorem
4.2 Remarks concerning Wilson’s theorem
and its converse and corollaries
4.3 Corollaries of Wilson’s 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 Kuiper’s theorem
6.4 Niven’s 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 Wilson’s 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 Meissel’s 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
Meissel’s 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 Bonse’s 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 Fermat’s numbers
14.3 Special problems and Fermat’s numbers
14.4 Another proof for Euclid’s theorem
14.5 Speed of the growth of Fermat’s
numbers
14.6 Fermat’s numbers and the problem of
inscribing regular polygons inside a circle
14.7 Refutation of Fermat’s assertion
and factorization of Fermat’s numbers
14.8 Mersenne’s numbers
14.9 Problems concerning Mersenne’s
numbers
14.10 Perfect, imperfect and redundant
numbers
14.11 Historical remarks concerning (even)
perfect numbers and Mersenne’s 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
Mersenne’s prime numbers and Fermat’s 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
Fermat’s numbers (  )
15.2 Definition of the set of Fermat’s
prime numbers by the prime number’s formula
15.3 Some general facts about Mersenne’s
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 Clement’s 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 Fermat’s 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
Fermat’s theorem
19.3. Chronology of Fermat’s theorem
19.4. Fermat’s theorem, for exponent 4
19.5. Fermat’s 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 Fermat’s
theorem  
20.2. Primitive, Algebraic and geometric
methods
20.3 An indirect proof of Fermat’s theorem
(elliptic curves)
20.4 Taniyama- Shimura – Weil conjecture
and Fermat last theorem
20.5 Theorems of Wiles and Taylor-Wiles
20.6 Latest achievements and fundamental
results concerning Fermat’s 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
Fermat’s 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
here
is the list of ISBN of some of my books below :
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Dictionary mathematics - 606 pages - ISBN : 964-436-941-6
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Basic mathematics - 348 pages - ISBN : 964-310-016-2
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Calculus - Editor - 311 pages - ISBN : 964-6214-42-8
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Calculus - Editor - 357 pages - ISBN : 964-6214-41-x
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Calculus - pages 347 - ISBN : 964-91766-6-7
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Calculus - pages 447 - 3rd impression - ISBN : 964-353-720-x
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Power and radical - 188 pages - 6th impression - ISBN :
964-353-852-4
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vectors - 150 pages - 4th impression - ISBN : 964-353-880-x
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Limit - 148 pages - 12th impression - ISBN : 964-385-003-x
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Defines of the domain and range functions - 135 pages - 13th
impression -ISBN : 964-385-114-1
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Olympiad mathematics - Editor - 208 pages - ISBN :
964-353-021-3
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The problems mathematics - 175 pages - ISBN : 964-6150-25-x
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