[18] **viXra:1505.0205 [pdf]**
*replaced on 2015-06-01 04:09:41*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

We diagnose the body of the critical strip. Thereby, we can extract the deterministic
location of the critical line.

**Category:** Number Theory

[17] **viXra:1505.0203 [pdf]**
*submitted on 2015-05-26 15:26:42*

**Authors:** Douadi MIHOUBI

**Comments:** 19 Pages.

Based on, the well-ordering (N,<) of the set of natural numbers N, and some basic concepts of number theory, and using the proof by contradiction and the inductive proof on N, we prove that the validity of the Goldbach's statement:
every even integer 2n > 4, with n > 2, is the sum of two primes.
This result confirms the Goldbach conjecture, which allows to inserting it as theorem in number theory.
Key Words: Well-ordering (N,<), basic concepts and theorems on number theory, the indirect and inductive proofs on natural numbers.
AMS 2010: 11AXX, 11p32, 11B37.

**Category:** Number Theory

[16] **viXra:1505.0194 [pdf]**
*submitted on 2015-05-26 10:28:26*

**Authors:** Lukas Saul

**Comments:** 5 Pages.

Some definitions and elementary theorems are given here describing tonal and nagual numbers, sets, and processes.

**Category:** Number Theory

[15] **viXra:1505.0170 [pdf]**
*submitted on 2015-05-24 11:59:01*

**Authors:** Kyle Den Hartog, The Human Species

**Comments:** 1 Page. Please leave the second author(s) "The Human Species" on there, this is intended to give credit for all so that it cannot be legally protected by any person.

This is a method of prime number verification. It is a pattern that is formed based upon the relationship of square numbers and prime numbers.

**Category:** Number Theory

[14] **viXra:1505.0156 [pdf]**
*replaced on 2017-05-28 07:56:58*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 1 Page.

In this paper, we analyze the anatomy of critical line.

**Category:** Number Theory

[13] **viXra:1505.0150 [pdf]**
*submitted on 2015-05-21 05:07:12*

**Authors:** Zhang Tianshu

**Comments:** 22 Pages.

In this article, first we classify A, B and C according to their respective odevity, and thereby ret rid of two kinds from AX+BY=CZ. Then affirmed AX+BY=CZ in which case A, B and C have a common prime factor by concrete examples. After that, proved AX+BY≠CZ in which case A, B and C have not any common prime factor by the mathematical induction with the aid of the symmetric law of odd numbers after the decomposition of the inequality. Finally, we have proved that the Beal’s conjecture does hold water after the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.

**Category:** Number Theory

[12] **viXra:1505.0144 [pdf]**
*submitted on 2015-05-20 11:30:31*

**Authors:** Marius Coman

**Comments:** 3 Pages.

The Smarandache-Coman function is the function defined on the set of non-null positive integers with values in the set of non-null positive integers in the following way: SC(n) is the least number such that SC(n)! is divisible by n + r, where r is the digital root of the number n. In other words, SC(n) = S(n + r), where S is the Smarandache function. I also state, in this paper, nine conjectures on this function which seems to be particularly interesting: beside other characteristics, it seems to have as values all the prime numbers and, more than that, they seem to appear, leaving aside the non-prime values, in natural order.

**Category:** Number Theory

[11] **viXra:1505.0119 [pdf]**
*replaced on 2015-05-16 10:19:18*

**Authors:** Marouane Rhafli

**Comments:** 7 Pages.

we introduce an algorithm that generates primes included in a given interval $I=[a,b]$ , the algorithm is an optimization to the segmented sieve of eratosthenes,it finds primes up to $N$ without any repetition of multiples of primes using the equation $p^{2}_{n}. p_{j}+2p_{n}.p{j}.c=N$ with $ c\in Z^{+}$ , its time complexity is sublinear $ O(nloglog(n)-n(loglog(n))^2)$.

**Category:** Number Theory

[10] **viXra:1505.0111 [pdf]**
*replaced on 2015-05-15 04:55:30*

**Authors:** T.Nakashima

**Comments:** 2 Pages.

The equivalent condition about mobius function
of The Generalized Riemann Hypothesis.

**Category:** Number Theory

[9] **viXra:1505.0107 [pdf]**
*submitted on 2015-05-13 23:34:42*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I conjecture that there exist an infinity of positive integers m of the form 6*k + 1 such that the numbers formed by concatenation n = m081 are primes or powers of primes, respectively semiprimes p*q such that q – p + 1 is prime or power of prime.

**Category:** Number Theory

[8] **viXra:1505.0106 [pdf]**
*submitted on 2015-05-14 00:58:51*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I conjecture that there exist an infinity of numbers ab formed by concatenation from a multiple of 30, a, and a square of a prime, b, which are primes or powers of primes, respectively semiprimes p*q such that q – p + 1 is prime or power of prime, respectively semiprimes p1*q1 such that q1 – p1 + 1 is semiprime p2*q2 such that q2 – p2 + 1 is prime or power of prime.

**Category:** Number Theory

[7] **viXra:1505.0104 [pdf]**
*submitted on 2015-05-13 09:53:42*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I conjecture that there exist an infinity of primes m such that the number n = m*(m + 360) – 6240 is square of prime, respectively prime, respectively semiprime p*q such that q – p + 1 is prime or square of prime, respectively semiprime p1*q1 such that q1 – p1 + 1 is a semiprime q2*p2 such that q2 – p2 + 1 is prime or square of prime.

**Category:** Number Theory

[6] **viXra:1505.0081 [pdf]**
*replaced on 2015-05-11 12:46:46*

**Authors:** Lukas Saul

**Comments:** 18 Pages. Minor typos fixed

We are transported to the infinite hotel via processes unknown and find a way to discuss with Georg Cantor himself the cardinality of infinite sets. Using Cantor's first theorem we enumerate the numbers between zero and one, and discover that Cantor's second theorem has not been proven with the rigor we expected and the diagonalization proof fails spectacularly for certain representations. However Cantor has the last laugh. Later we visit the large but finite hotel and discover that transcendental numbers of certain classes are in fact countable, and that uncountable infinites are only created by the addition of a class of numbers or objects we describe as nagual.

**Category:** Number Theory

[5] **viXra:1505.0077 [pdf]**
*submitted on 2015-05-10 11:34:55*

**Authors:** Alexander S. Nudelman

**Comments:** 5 Pages.

In this paper we formulate an intuitive Hypothesis about a new aspect of a well known method called “Sieve of Eratosthenes” and then prove that set of natural numbers N = {1, 2, . . .} contains infinite number of pairs of twin primes.

**Category:** Number Theory

[4] **viXra:1505.0044 [pdf]**
*submitted on 2015-05-05 23:48:14*

**Authors:** DaeHyeon KANG

**Comments:** 2 Pages.

Euclid's formula is fundamental and looks briefly, but We generate the pythagorean triple by this formula is not easy. therefore, I found the new formula to get the pythagorean triple easily

**Category:** Number Theory

[3] **viXra:1505.0038 [pdf]**
*submitted on 2015-05-04 22:10:43*

**Authors:** Pratish R. Rao, Prashanth R. Rao

**Comments:** 2 Pages.

In this paper we present a potentially novel partition generating algorithm for a positive integer k= k1k2.…kn-1kn . In previous papers we used a similar strategy to derive two important known mathematical results regarding factorials and a novel strategy to partition odd composites(Refs 1-3). Here we will generalize this approach to make it widely applicable to all positive integers. We believe this strategy may be an important tool to mathematicians to attack unsolved conjectures as well to derive alternate possibly simpler proofs of established theorems.

**Category:** Number Theory

[2] **viXra:1505.0030 [pdf]**
*submitted on 2015-05-03 14:31:32*

**Authors:** Chenglian Liu

**Comments:** 7 Pages.

In 2015, Liu et al. proposed a study relationship between RSA public key cryptosystem and Goldbach's conjecture properties. They discussed the relationship between RSA and Goldbach conjecture, twin prime and Goldbach conjecture. In this paper the author will extend to introduce the relationsip among Goldbach conjecture, twin prime and Fibonacci number. Based on their contribution, the author completely lists all combinations of twin prime in Goldbach conjecture.

**Category:** Number Theory

[1] **viXra:1505.0001 [pdf]**
*submitted on 2015-05-01 00:12:18*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make three conjectures regarding the infinity of prime terms respectively the infinity of a certain kind of semiprime terms of the sequence obtained concatenating the odd powers of the number 2 to the left respectively to the right with the digit 1.

**Category:** Number Theory