[11] **viXra:1902.0332 [pdf]**
*submitted on 2019-02-21 03:55:20*

**Authors:** Toshiro Takami

**Comments:** 5 Pages.

product [prime (n) ^ s / (prime (n) ^ s - 1), {n, 39001, 40000}], [s = 0.5 + i 14.1347]
Because there was capacity limitation of the computer, I divided it up to 40000, but there was no convergence trend.
This seems to be a conspiracy by ζ stars.

**Category:** Number Theory

[10] **viXra:1902.0235 [pdf]**
*submitted on 2019-02-13 05:23:19*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 6 Pages. Submitted to the The Ramanujan Journal. Comments welcome.

In this paper, we consider the abc conjecture in the case c=a+1. Firstly, we give the proof of the first conjecture that c

**Category:** Number Theory

[9] **viXra:1902.0200 [pdf]**
*submitted on 2019-02-11 06:24:07*

**Authors:** Faisal Amin Yassein Abdelmohssin

**Comments:** 2 Pages.

I claim that the sum of following distinct proper fractions [(1/2),(1/3),(1/6)] is the only triple of distinct proper fraction that sum to 1 {i.e. [(1/2)+(1/3)+(1/6)]=1}.

**Category:** Number Theory

[8] **viXra:1902.0188 [pdf]**
*replaced on 2019-02-18 21:44:57*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

I proved Riemann hypothesis.
It proved that it never takes a zero point if a<0.5, 0.5<a.
There are many zeros such as 0.5+i14.1347, but all the known zero points are on the 0.5 axis.
I used the smallest prime number 2.

**Category:** Number Theory

[7] **viXra:1902.0147 [pdf]**
*submitted on 2019-02-08 09:11:21*

**Authors:** Kenneth A. Watanabe

**Comments:** 13 Pages.

The Near-Square Prime conjecture, states that there are an infinite number of prime numbers of the form x^2 + 1. In this paper, a function was derived that determines the number of prime numbers of the form x^2 + 1 that are less than n^2 + 1 for large values of n. Then by mathematical induction, it is proven that as the value of n goes to infinity, the function goes to infinity, thus proving the Near-Square Prime conjecture.

**Category:** Number Theory

[6] **viXra:1902.0117 [pdf]**
*replaced on 2019-02-16 16:23:30*

**Authors:** Toshiro Takami

**Comments:** 10 Pages.

Although the calculation result of zeta comes out immediately, it was found out that it seems that it calculates by the expression as shown below when examining what kind of calculation method is used integrally.
If I had calculated according to the method in Introduction, I thought that it would take a very long time to calculate zeta, I studied mysteriously.
However, it is judgmental as to whether this investigation result is true or not.
If this calculation method is used, it is natural that a zero point appears only on 0.5.
As an overview of the net, it seems that the following formula is frequently used for calculation of Riemann zeta function.
In this calculation method, there is no zero point other than 0.5.
The mystery of 150 years has been solved.
End of Riemann Hypothesis proof.
ζ(s)＝π^(s-1/2)Γ((1-s)/2)／Γ(s/2)ζ(1-s), s=a+bi

**Category:** Number Theory

[5] **viXra:1902.0106 [pdf]**
*replaced on 2019-02-10 10:53:42*

**Authors:** Algirdas Antano Maknickas

**Comments:** 2 Pages.

This remark gives analytical solution of Last Fermat's Theorem

**Category:** Number Theory

[4] **viXra:1902.0040 [pdf]**
*submitted on 2019-02-02 16:34:38*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 9 Pages. A Complete proof of the abc conjecture using elementary calculus with numerical examples. Submitted to the Ramanujan Journal. Your comments are welcome.

In this paper, we consider the abc conjecture. Firstly, we give a proof of a first conjecture that c

**Category:** Number Theory

[3] **viXra:1902.0036 [pdf]**
*submitted on 2019-02-03 00:15:01*

**Authors:** Simon Plouffe

**Comments:** 10 Pages.

Une famille de formules permettant d'obtenir une suite de longueur arbitraire de nombres premiers. Ces formules sont nettement plus efficaces que celles de Mills ou Wright. Le procédé permet de produire par exemple une suite dont la croissance est double exponentielle mais l'exposant = 101/100.

**Category:** Number Theory

[2] **viXra:1902.0020 [pdf]**
*replaced on 2019-02-03 20:29:25*

**Authors:** Toshiro Takami

**Comments:** 174 Pages.

I also found a zero point which seems to deviate from 0.5.
I thought that the zero point outside 0.5 can not be found very easily in the area which can not be shown in the figure, but this area can not be represented in the figure but can be found one after another.
It is completely unknown whether this axis is distorted in the 0.5 axis or just by coincidence.
The number of zero points in the area that can not be shown in the figure is now 43.
No matter how you looked it was not found in other areas.
It seemed that there is no other way to interpret this axis as 0.5 axis is distorted in this area.
Somewhere on the net there is a memory that reads the mathematician's view that "there are countless zero points in the vicinity of 0.5 on high area".
We are reporting that the zero point search of the high-value area of the imaginary part which was giving up as it is no longer possible with the supercomputer is no longer possible, is reported.
43 zero-point searches in the high-value area of the imaginary part are thus successful.
This means that the zero point search in the high-value area of the imaginary part has succeeded in the 43.
We will also write 43 zero point searches of the successful high-value area of the imaginary part.
There are many counterexamples far beyond 0.5, which is far beyond the limit, but the computer can not calculate it.
Moreover, I believe that it can only be confirmed on supercomputer whether this is really counterexample. In addition, it is necessary to make corrections in the supercomputer.

**Category:** Number Theory

[1] **viXra:1902.0005 [pdf]**
*replaced on 2019-02-19 08:32:39*

**Authors:** James Edwin Rock

**Comments:** 2 pages of exposition and 7 pages with supporting tables. This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Let P_n be the n_th prime. For twin primes P_n – P_(n-1) = 2. Let X be the number of (6j –1, 6j+1) pairs in the interval [P_n, P_n^2]. The number of twin primes (TPAn) in [P_n, P_n^2] can be approximated by the formula
(a_3 /5)(a_4 /7)(a_5 /11)…(a_n /P_n)(X) for 3 ≤ m ≤ n, a_m = P_m –2 .
We establish a lower bound for TPAn (3/5)(5/7)(7/9)…(P_n–2)/P_n)(X) = 3X/P_n < TPAn.
We exhibit a formula showing as P_n increases, the number of twin primes in the interval [P_n, P_n^2] also increases. Let P_n – P_(n-1) = c. For all n (TPAn-1)(1+(2c –2)/2P_(n-1)+(c^2–2c)/2P_(n-1)^2) < TPAn

**Category:** Number Theory