[15] **viXra:1210.0176 [pdf]**
*replaced on 2013-05-19 12:21:19*

**Authors:** Zeraoulia Elhadj

**Comments:** 12 Pages.

In this paper, a positive answer to the Riemann hypothesis is given by using a new result predicting the exact location of zeros of the alternating zeta function on the critical strip.

**Category:** Number Theory

[14] **viXra:1210.0167 [pdf]**
*replaced on 2013-02-23 09:25:37*

**Authors:** Cristian Dumitrescu

**Comments:** 8 Pages.

In this paper, I present a connection between the Riemann Hypothesis and model theory, and this connection leads to a solution to the Riemann Hypothesis.

**Category:** Number Theory

[13] **viXra:1210.0157 [pdf]**
*submitted on 2012-10-27 01:10:44*

**Authors:** Diego Alonso Cortez

**Comments:** 9 Pages.

We compute the primes up to 1 million by starting an arithmetic progression at every positive integer 2n, that grows by n, where n > 1. All numbers not in the progression are prime.

**Category:** Number Theory

[12] **viXra:1210.0148 [pdf]**
*replaced on 2014-09-17 10:43:16*

**Authors:** Bertrand Wong

**Comments:** 4 Pages.

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper approaches the twin primes problem through the analysis of the intrinsic nature of the prime numbers.

**Category:** Number Theory

[11] **viXra:1210.0147 [pdf]**
*replaced on 2014-09-18 12:08:54*

**Authors:** Bertrand Wong

**Comments:** 6 Pages.

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper approaches the twin primes problem through the analysis of the composite numbers.

**Category:** Number Theory

[10] **viXra:1210.0140 [pdf]**
*replaced on 2012-10-25 10:11:22*

**Authors:** Patrick A Devlin

**Comments:** 17 Pages.

In number theory, and especially the study of the diophantine approximation, the Lonely Runner Conjecture is a conjecture with important and widespread applications in mathematics.
A previous paper by this author proved the lonely runner conjecture for any n, for the special case of integers with particularly correlated prime factors. In this paper we attempt to extend this work to the general case of n arbitrary integers. The paper demonstrates that a set of integers with correctly correlated prime factors, such that they satisfy the conjecture, can be modified to approximate any set of arbitrary integers with infinite precision.

**Category:** Number Theory

[9] **viXra:1210.0125 [pdf]**
*submitted on 2012-10-22 16:16:11*

**Authors:** C. G. Provatidis

**Comments:** 13 Pages.

This paper reveals that the reference function G(2n)=2n/(ln(n))^2 plays a significant role in the distribution of the total number of pairs (p, q) of primes that fulfill the condition (p + q = 2n), which constitutes Goldbach’s conjecture. Numerical experiments up to 2n=500,000 show that, in the plot of the number of pairs versus 2n, the ratio of the lowest points over G(2n) tends asymptotically to the value 2/3. The latter fact dictates that the lower bound concerning the minimum number of pairs that fulfill Goldbach’s conjecture is equal to 4n/[3(ln(n))^2]. Moreover, smoothed sequences by treatment of the aforementioned pairs are revealed.

**Category:** Number Theory

[8] **viXra:1210.0112 [pdf]**
*replaced on 2012-10-25 09:56:10*

**Authors:** Patrick A Devlin

**Comments:** 5 Pages.

In number theory, and especially the study of the diophantine approximation, the Lonely Runner Conjecture is a conjecture with important and widespread applications in mathematics.
This paper attempts to prove the conjecture for any n runners in the special case of integers with particularly correlated prime factors.

**Category:** Number Theory

[7] **viXra:1210.0066 [pdf]**
*submitted on 2012-10-13 02:19:06*

**Authors:** C. G. Provatidis

**Comments:** 3 Pages.

In this short paper we reveal a sequence of three smoothing procedures related to Goldbach’s conjecture. While the cloud of points that represent the number of pairs (p, q), which fulfill the conjecture p+q=2n, versus 2n occupies a quite broad area of curvilinear triangular shape, suitable averages can reduce it into oscillating lines with progressively decreasing amplitudes.

**Category:** Number Theory

[6] **viXra:1210.0048 [pdf]**
*submitted on 2012-10-10 02:57:48*

**Authors:** Chun-Xuan Jiang

**Comments:** 4 Pages.

see paper for abstract in Chinese

**Category:** Number Theory

[5] **viXra:1210.0027 [pdf]**
*submitted on 2012-10-06 14:11:49*

**Authors:** Chun-Xuan Jiang

**Comments:** 5 Pages.

用最简单初等数学证明了费马大定理

**Category:** Number Theory

[4] **viXra:1210.0026 [pdf]**
*submitted on 2012-10-06 10:36:09*

**Authors:** Viktor K

**Comments:** 5 Pages.

In this paper, we present a resolution to the problem of the Riemann Hypothesis. In particular, by the use of the Mellin integral transform and analytic techniques, we prove there exist no zeros to the Riemann Zeta Function in the critical strip outside the line whose real component is 1/2.

**Category:** Number Theory

[3] **viXra:1210.0017 [pdf]**
*submitted on 2012-10-04 00:00:42*

**Authors:** Tian-Chou Wang

**Comments:** 69 Pages. Manuscript scan, in Chinese, and copyright belongs to the author.

This is a part of Dr. Tian-Chou Wang's proof to Riemann Hypothesis. It follows 'the opening' (viXra citation number: 1209.0063), Chapter 1 (viXra citation number: 1209.0068), Chapter 2 (viXra citation number: 1209.0078), Chapter 3 (viXra citation number: 1209.0090), Chapter 4 (viXra citation number: 1209.0100), Chapter 5 (viXra citation number: 1210.0008), Chapter 6 (viXra citation number: 1210.0013), and this is the end of Section One.

**Category:** Number Theory

[2] **viXra:1210.0013 [pdf]**
*submitted on 2012-10-02 20:57:43*

**Authors:** Tian-Chou Wang

**Comments:** 48 Pages. Manuscript scan, in Chinese, and copyright belongs to the author.

This is a part of Dr. Tian-Chou Wang's proof to the Riemann Hypothesis. It follows 'the opening' (viXra citation number: 1209.0063), Chapter 1 (viXra citation number: 1209.0068), Chapter 2 (viXra citation number: 1209.0078), Chapter 3 (viXra citation number: 1209.0090), Chapter 4 (viXra citation number: 1209.0100), Chapter 5 (viXra citation number: 1210.0008)

**Category:** Number Theory

[1] **viXra:1210.0008 [pdf]**
*submitted on 2012-10-01 19:09:51*

**Authors:** Tian-Chou Wang

**Comments:** 51 Pages. Manuscript scan, in Chinese, and copyright belongs to the author.

This is a part of Dr. Tian-Chou Wang's proof to the Riemann Hypothesis. It follows 'the opening' (viXra citation number: 1209.0063), Chapter 1 (viXra citation number: 1209.0068), Chapter 2 (viXra citation number: 1209.0078), Chapter 3 (viXra citation number: 1209.0090), Chapter 4 (viXra citation number: 1209.0100)

**Category:** Number Theory