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
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
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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
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Book of the discovery of prime numbers
formula and its results
Freely
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The book of the discovery
of prime numbers formula and its results
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 Bertrands principle and theorems of
Chebyshev, Dirichlet and Poisson..............................................................................................35
1.11 Lagranges
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 Stochastics
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 Wilsons theorem and its consequences
...............................................
66
4.1 Wilsons theorem
...................................................................................................................................................................................................... 67
4.2 Remarks concerning Wilsons theorem
and its converse and corollaries.............................................................................................
69
4.3 Corollaries of Wilsons
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 Millss
theorem..............................................................................
87
6.3 Kuiperss
theorem.........................................................................
87
6.4 Nivens
theorem.............................................................................
88
6.5 Formulas of generating prime
numbers................................... . 88
6.6 Generalized Millss
theorem..................................................
.... 92
6.7 Investigation into
polynomials................................................... 94
6.8 A formula presenting for
generating prime numbers by Wilsons
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 Riemanns 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 Fermats
numbers...................................................................
149
14.3 Special problems and Fermats
numbers........................... 154
14.4 Another proof for Euclids
theorem......................................
157
14.5 Speed of the growth of Fermats
numbers............................ 157
14.6 Fermats numbers and the problem of
inscribing regular polygons inside a circle
158
14.7 Refutation of Fermats assertion
and factorization of Fermats
numbers
159
14.8 Mersennes
numbers...............................................................
159
14.9 Problems concerning Mersennes
numbers.......................... 160
14.10 Perfect, imperfect and redundant
numbers............................ 161
14.11 Historical remarks concerning (even)
perfect numbers and Mersennes
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
Mersennes prime numbers and Fermats 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
Fermats numbers ()......
...
178
15.2 Definition of the set of Fermats
prime numbers by the prime numbers formula
............................................................................................
178
15.3 Some general facts about Mersennes
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 Hardys
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 Clements 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 Fermats 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
Fermats last theorem
......................................................................................................................................203
19.3 Chronology of Fermats last
theorem........................................................................................................................................................................
. 204
19.4 Sophie Germains
theorem...........................................................................................................................................................................................218
19.5 Fermats last theorem for exponent
"4".....................................................................................................................................................................
221
19.6 Fermats 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 Fermats
last theorem 
..........................................................................................................................
..
230
20.2. Primitive, Algebraic and geometric
methods.......................................................................................................................................................
.. 231
20.3 An indirect proof of Fermats 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 Fermats 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
Fermats 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
Wilsons, Fermats and Eulers 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 Riemanns 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 Mersennes prime numbers set by using the prime numbers
generator
............333
22.13 A program for determining the
Mersennes prime numbers of M-digits (M: Arbitrary
number)............................................................................ 334
22.14 The New Mersennes 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
)
functions
and
functions are discovered by discoverer (Prof.S.M.R.Hashemi
Moosavi). The software of this function is produced.
