[17] **viXra:1912.0225 [pdf]**
*submitted on 2019-12-12 05:58:40*

**Authors:** Surajit Ghosh

**Comments:** 41 Pages.

Riemann hypothesis stands proved in three diﬀerent ways.To prove Riemann hypothesis from the functional equation concept of Delta function is introduced similar to Gamma and Pi function. Other two proofs are derived using Eulers formula and elementary algebra. Analytically continuing gamma and zeta function to an extended domain, poles and zeros of zeta values are redeﬁned.

**Category:** Number Theory

[16] **viXra:1912.0208 [pdf]**
*submitted on 2019-12-10 23:15:55*

**Authors:** Aaron chau

**Comments:** 2 Pages.

然而黎曼的假设，挥之不去地刺激了世界各民族的数学家。 但他们在受到了刺激之后，究竟干了一些什么呢？
可惜有些人还在把伪造质数说成是“数学主流”, 并又靠伪造质数来争取学位，难道数学的主流就是伪造质数？
也事实上推翻黎曼假设需要越筒单越有智慧的算术。

**Category:** Number Theory

[15] **viXra:1912.0207 [pdf]**
*submitted on 2019-12-11 01:03:26*

**Authors:** Toshiro Takami

**Comments:** 9 Pages.

I considered the Twin Prime Conjecture.
The probability twin prime approximately is slightly lower than 4/3 times the square of the probability that a prime will appear in.\\
When the number grows to the limit, the primes to be produced rarely, but since Twin Primes are slightly lower than 4/3 times the square of the distribution of primes, the frequency of production of Twin Primes is very equal to 0.\\
The places where prime numbers come out are filled with multiples of primes one after another, and eventually disappear almost.\\
Primes can only occur very rarely when the numbers are huge.\\
This is natural from the following equation.\\
\begin{equation}
\pi(x)\sim\frac{x}{\log{x}}\ \ \ (x\to\infty)
\end{equation}\\
$[Probability\ of\ the\ Existence\ of\ primes]^2\times4/3\sim$
(Probability\ of\ the\ Existence\ of\ Twin\ Primes)\\
When the number becomes extreme, the generation of primes becomes extremely small. However, it is not 0.\\
Very few, but primes are generated.\\
If the twin primes appears as two primes completely independently, Twin Prime Problem is denied.\\
However, if twin primes appear in combination and appear like primes, twin primes consist forever and Twin Prime Problem is correct.\\

**Category:** Number Theory

[14] **viXra:1912.0205 [pdf]**
*submitted on 2019-12-11 02:48:40*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

There are almost no primes in the infinite world.
This is because the place where the primes appears is occupied by multiple of the primes.
If you think about a hexagon, you can see it right away.

**Category:** Number Theory

[13] **viXra:1912.0194 [pdf]**
*submitted on 2019-12-10 04:23:59*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 82 Pages.

In this research thesis, we have analyzed further Ramanujan formulas and described new possible mathematical connections with some parameters of Particle Physics and Cosmology

**Category:** Number Theory

[12] **viXra:1912.0174 [pdf]**
*submitted on 2019-12-08 21:14:39*

**Authors:** Takamasa Noguchi

**Comments:** 8 Pages.

I made an approximate formula.
In the formula, when N is small, the accuracy is very bad, but as N increases, the accuracy also improves.

**Category:** Number Theory

[11] **viXra:1912.0157 [pdf]**
*replaced on 2019-12-08 21:38:41*

**Authors:** Toshiro Takami

**Comments:** 9 Pages.

I proved the Twin Prime Conjecture.
The probability that (6n -1) is a prime and (6n+1) is also a prime approximately is slightly lower than 4/3 times the square of the probability that a prime will appear in.
I investigated up to 5$\times10^{12}$.\\
All Twin Primes are produced in hexagonal circulation. It does not change in a huge number (forever huge number).\\
The production of Twin Primes equal the existence of Twin Primes.\\
When the number grows to the limit, the primes to be produced rarely, but since Twin Primes are slightly lower than 4/3 times the square of the distribution of primes, the frequency of production of Twin Primes is very equal to 0.\\
However, it is not 0. Because, primes continue to be produced. Therefore, Twin Primes continue to be produced.\\
If the Twin Primes is finite, the primes is finite.\\
This is because slightly lower than 4/3 times the square of the probability of primes is the probability of Twin Primes.
This is contradiction.
Because there are an infinite of primes.\\

**Category:** Number Theory

[10] **viXra:1912.0153 [pdf]**
*replaced on 2019-12-08 07:55:05*

**Authors:**

**Comments:** Pages. Correction to first version (v1) is to replace COS with SIN in the third vector, marked as (3)

No zeta zero is off the critical line.

Riemann Hypothesis is false if and only if A, B and C are coplanar.

A and B are geometrical objects directly related to (supposed symmetric distinct) zeta roots and C is derived from A and B.

The proof shows that A, B and C are linearly independent, so not coplanar.

**Category:** Number Theory

[9] **viXra:1912.0151 [pdf]**
*submitted on 2019-12-08 01:15:38*

**Authors:** Toshiro Takami

**Comments:** 8 Pages.

If (p,p+2) are twin primes, (p+30, p+2+30) or (p+60, p+2+60) or (p+90, p+2+90) or (p+120, p+2+120) or (p+150, p+2+150) ) or (p+180, p+2+180) or (p+210, p+2+210) or (p+240, p+2+240)……. is to be a twin primes.\\
There are three type of twin primes, last numbers are (1, 3)..(7, 9)..(9, 1).\\
They are lined up at intervals such as 30 or 60 or 90 or 120 or 150 or 180 or 210 or 240 or 270 or 300 etc.\ That is, it is a multiple of 30. \\
Repeat this.\\
And the knowledge about prime numbers is also taken into account.\\
That is, Twin Primes exist forever.\\

**Category:** Number Theory

[8] **viXra:1912.0148 [pdf]**
*submitted on 2019-12-08 06:34:20*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 147 Pages.

In this research thesis, we have analyzed further Ramanujan formulas and described new possible mathematical connections with some sectors of Particle Physics (values of Pion mesons and other baryons and mesons) and Cosmology

**Category:** Number Theory

[7] **viXra:1912.0124 [pdf]**
*replaced on 2019-12-10 22:57:48*

**Authors:** Ninh Khac Son

**Comments:** 5 Pages.

Goldbach’s conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: ”Every even integer greater than 2 can be expressed as the sum of two primes”.\\ Manuscript content: Prove that Goldbach’s conjecture is correct

**Category:** Number Theory

[6] **viXra:1912.0119 [pdf]**
*submitted on 2019-12-06 02:07:40*

**Authors:** Takamasa Noguchi

**Comments:** 4 Pages. Explanation of effective prime number judgment method even for Carmichael number.

Explanation of effective prime number judgment method even for Carmichael number.
This method of judgment does not give a 100% correct answer.
Care must be taken especially for (n=p^k (P=Prime)) with primitive roots.

**Category:** Number Theory

[5] **viXra:1912.0117 [pdf]**
*submitted on 2019-12-06 04:20:47*

**Authors:** Matanari Shimoinuda

**Comments:** 32 Pages.

In this article, we review the local Langlands program. I hope that this article is a useful guide to understand Langlands program.

**Category:** Number Theory

[4] **viXra:1912.0108 [pdf]**
*submitted on 2019-12-06 06:49:41*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 83 Pages.

In this research thesis, we have analyzed further Ramanujan formulas and described new possible mathematical connections with some sectors of Particle Physics and Cosmology

**Category:** Number Theory

[3] **viXra:1912.0087 [pdf]**
*submitted on 2019-12-05 05:25:17*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 133 Pages.

In this research thesis, we have analyzed further Ramanujan formulas and described new possible mathematical connections with some sectors of Particle Physics and Cosmology

**Category:** Number Theory

[2] **viXra:1912.0082 [pdf]**
*replaced on 2019-12-12 06:34:16*

**Authors:** John Yuk Ching Ting

**Comments:** 49 Pages. Reverse-engineered Rigorous proofs for Riemann hypothesis (and explaining the two types of Gram points) and Polignac's and Twin prime conjectures.

Mathematics for Incompletely Predictable Problems is associated with Incompletely Predictable problems containing Incompletely Predictable entities. Nontrivial zeros and two types of Gram points in Riemann zeta function (or its proxy Dirichlet eta function) together with prime and composite numbers from Sieve of Eratosthenes are Incompletely Predictable entities. Correct and complete mathematical arguments for first key step of converting this function into its continuous format version, and second key step of applying Information-Complexity conservation to this Sieve result in direct spin-offs from first key step consisting of proving Riemann hypothesis (and explaining two types of Gram points), and second key step consisting of proving Polignac's and Twin prime conjectures. We justify our Reverse-Engineered proofs and explanations.

**Category:** Number Theory

[1] **viXra:1912.0028 [pdf]**
*submitted on 2019-12-02 13:53:35*

**Authors:** BOUARFAOUI Saïd

**Comments:** 8 Pages. Some studies on the 3n+1 problem

In the present paper, we study the 3n+1 problem to know if there is a theoretical number such as the number never land on the cycle {4;2;1}and grows continually.We will specify the general formula such as the number of uneven steps (3��+1)and even steps (��/2)are equals.We want to know also the uneven number form 2^��+2^0 and its composition during ��uneven (3��+1)and even steps (��/2).The composition number 2��+20will be viewed in two ways :1. When the powers which compose the numbers are expanded. We will recognize the Pascal’s triangle.2. When the powers which compose the numbers are agglutinate. We will recognize (3^��) in base 2.

**Category:** Number Theory