[17] **viXra:1606.0345 [pdf]**
*submitted on 2016-06-30 11:00:58*

**Authors:** Scott B. Guthery

**Comments:** 8 Pages.

An algorithm for recursively generating the sequence of solutions of a prime constellation is described. The algorithm is based on an polynomial equation formed from the first n elements of the constellation. A root of this equation is the next element of the sequence.

**Category:** Number Theory

[16] **viXra:1606.0327 [pdf]**
*submitted on 2016-06-29 07:46:25*

**Authors:** Mohamed Ouiter

**Comments:** 7 Pages.

From the definition that a number is Prime if he admits that two dividers and any number not prime can it write as a product of prime factors, I was able to identify a simple law that governs the distribution of prime numbers.

**Category:** Number Theory

[15] **viXra:1606.0310 [pdf]**
*submitted on 2016-06-28 09:09:00*

**Authors:** Peter Bissonnet

**Comments:** 14 Pages.

When a subset of sequential integers is arranged in a specific way, there appears a paired set of slanted straight lines along which prime numbers seem to naturally arrange themselves in a repeated fashion. This arrangement can further be observed to be a two dimensional surface applicable to the cylinder. If this arrangement is on a piece of paper, then one can fold the paper in the form of a cylinder, and the paired set of slanted straight lines unite at the page edges to form a double helix winding down the cylinder. Paired primes are thus seen to be an association between primes residing on these two paired helixes, and further analysis shows that there appears to be two types of paired primes. Is the prime number double helix nature’s secret for jump starting life (DNA) and thereby defeating entropy (at least in the initial stage) by creating order from order instead of order from disorder? The prime number trends examined exhibit right handed chirality; left handed chirality is obtained by symmetry considerations.

**Category:** Number Theory

[14] **viXra:1606.0306 [pdf]**
*submitted on 2016-06-28 09:30:16*

**Authors:** Peter Bissonnet

**Comments:** 2 Pages. This is a Russian journal named "Almanac of Modern Science and Education" and can be found at the following link: http://www.gramota.net/eng/editions/5.html

This very short paper illustrates a mathematical method which illustrates the possibility of reducing a prime product (N = PQ) from two independent variables, namely the two original prime numbers P and Q, to only one independent variable which determines both prime numbers.

**Category:** Number Theory

[13] **viXra:1606.0302 [pdf]**
*replaced on 2016-07-21 20:07:29*

**Authors:** T.Nakashima

**Comments:** 2 Pages.

reration of recurring decimal and primitive root

**Category:** Number Theory

[12] **viXra:1606.0184 [pdf]**
*submitted on 2016-06-17 22:38:57*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 18 Pages.

In this research investigation, the author has presented a theory of ‘Universal
Relative Metric That Generates A Field Super-Set To The Fields Generated By
Various Distinct Relative Metrics’.

**Category:** Number Theory

[11] **viXra:1606.0173 [pdf]**
*submitted on 2016-06-17 08:50:55*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 16 Pages.

In this research investigation, the author has presented a theory of ‘Universal
Holistic Beauty Primality Tree Of Any Set, Universal Growth Of Any Given Set’.

**Category:** Number Theory

[10] **viXra:1606.0154 [pdf]**
*submitted on 2016-06-15 07:31:44*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 14 Pages.

In this research investigation, the author has presented a theory of ‘The Universal
Irreducible Any Field Generating Metric’.

**Category:** Number Theory

[9] **viXra:1606.0144 [pdf]**
*replaced on 2016-06-24 21:17:25*

**Authors:** Anthony J. Browne

**Comments:** 5 Pages.

A form of the exponential Mangoldt function is derived using indicator functions. The function's relationship to other important number theoretic functions are derived and discussed.

**Category:** Number Theory

[8] **viXra:1606.0136 [pdf]**
*submitted on 2016-06-14 00:55:44*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 13 Pages.

In this research investigation, the author has presented a theory of ‘The Universal Irreducible Any Field Generating Metric’.

**Category:** Number Theory

[7] **viXra:1606.0135 [pdf]**
*submitted on 2016-06-14 00:58:08*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 13 Pages.

In this research investigation, the author has presented a theory of ‘The Universal Irreducible Any Field Generating Metric’.

**Category:** Number Theory

[6] **viXra:1606.0118 [pdf]**
*replaced on 2016-06-13 05:09:24*

**Authors:** Reuven Tint

**Comments:** 12 Pages. Original written Russian

Let us prove that invariant identity is used for the proof of the FLT and Beal conjecture.

**Category:** Number Theory

[5] **viXra:1606.0109 [pdf]**
*submitted on 2016-06-11 15:07:52*

**Authors:** William R. Blickos

**Comments:** 12 Pages.

This paper provides a method using periodic functions to check for primality, count factors, list factors,
calculate the exact prime distribution, and determine the Nth prime. It describes this method in a straightforward
manner, from one equation to the next, using graphs between each key step to help quickly visualize the
reasoning and result of each maneuver. It concludes with brief afterthoughts and ongoing questions about the
technique.

**Category:** Number Theory

[4] **viXra:1606.0108 [pdf]**
*submitted on 2016-06-11 15:09:58*

**Authors:** William R. Blickos

**Comments:** 4 Pages.

A Trigonometric Series is crafted that gives the number of factors of x for all x. It is then manipulated to list all those factors. It is then used to give the exact distribution of the primes. It is then changed into a recursive sequence that generates the nth prime. Finally, a Product Polynomial Series is suggested as an improved alternative to the original. There is a series of questions in the second section regarding the functions.

**Category:** Number Theory

[3] **viXra:1606.0088 [pdf]**
*submitted on 2016-06-09 13:43:39*

**Authors:** Hitesh Jain

**Comments:** 4 Pages.

To find out necessary conditions for any number to be expressed as difference of 4th powers of 2 natural numbers and maximum number of ways.

**Category:** Number Theory

[2] **viXra:1606.0072 [pdf]**
*submitted on 2016-06-07 11:02:32*

**Authors:** William R. Blickos

**Comments:** 7 Pages.

Surfaces representing the primes and composites, the upper twin prime, the difference between squares, and the relations among them, are used to select input for a quadratic in such a way as to always generate a Twin Prime. Because each input generates a unique Twin, and because the input set is infinite, there are infinitely many twin primes.

**Category:** Number Theory

[1] **viXra:1606.0065 [pdf]**
*replaced on 2017-12-07 17:54:27*

**Authors:** Igor Turkanov

**Comments:** 27 Pages.

This theorem is based on holomorphy of studied functions and the fact that nearby of a singularity point the real part of some rational function can take random arbitrary preassigned value.

**Category:** Number Theory