Number Theory

1308 Submissions

[9] viXra:1308.0122 [pdf] replaced on 2013-08-28 08:48:38

Symmetry Distribution Law of Prime Numbers on Positive Integers and Related Results

Authors: Yibing Qiu
Comments: 6 Pages.

Abstract This article puts forward a new theorem concerns the distribution of prime numbers: Let integer n≥4, there exist two distinct odd primes p and q such that n﹣p＝q﹣n. Proves the theorem establish applied the Congruence theory and the Fermat's method of infinite descent. With the application of the theorem, reaches several results.
Category: Number Theory

[8] viXra:1308.0077 [pdf] submitted on 2013-08-15 10:34:17

Proof for the 9 to 1 Twin Primes

Authors: Lenient T Tavengwa
Comments: 2 Pages.

The twin primes conjecture asserts that there are infinitely many primes p such that p + 2 is also prime. The present paper proves that.
Category: Number Theory

[7] viXra:1308.0074 [pdf] submitted on 2013-08-14 13:04:58

Proof of the Infinite of the Twinprimes (New Called Primeangels)

Authors: Th. Guyer
Comments: 1 Page.

Euklid's Theorem (of the infinite of the PrimeNumbers) is given; where p=prim and the TwinPrime(s) are called PrimeAngels. So P(rime)=P(rime) / P(rime)=N(o)P(rime); P/=NP is no longer available and the problem was hard for more than 2000 years!
Category: Number Theory

[6] viXra:1308.0071 [pdf] submitted on 2013-08-14 00:20:19

Zeros Distribution of the Riemann Zeta-Function

Authors: Kairbek Kazbekov
Comments: 27 Pages.

Horizontal and vertical distributions of complex zeros of the Riemann zeta-function in the critical region are being found in general form in the paper on the basis of standard methods of function theory of complex variable.
Category: Number Theory

[5] viXra:1308.0055 [pdf] replaced on 2013-09-06 02:23:31

There Are Infinitely Many Primes of the Form αβn+χ ,αnβ+χ and αβ1nmβ2+χ

Authors: Zhen Liu
Comments: 12 Pages.

Using the method for equation reconstruction of prime sequence, this paper gives the proof that there are infinitely many primes of the form αβn+χ ,αnβ+χ and αβ1nmβ2+χ.
Category: Number Theory

[4] viXra:1308.0045 [pdf] submitted on 2013-08-08 21:01:21

An Elegant Proof that the Catalan’s Constant is Irrational

Authors: Edigles Guedes
Comments: 2 Pages.

We use the contradiction method for prove that the Catalan’s constant is irrational.
Category: Number Theory

[3] viXra:1308.0032 [pdf] submitted on 2013-08-05 18:39:33

Using Probabilities of Prime Number Theorem to Prove Goldbach's Conjecture

Authors: Dmitri Abramov
Comments: 5 Pages.

This article will define the range in which there is at least one pair of odd primes that when added produce specific even number. It will prove that every even number in that range can be written as a sum of at least one pair of odd primes. Additionally, this paper will prove trivial soft versions of Goldbach's conjecture that follow from the hard version.
Category: Number Theory

[2] viXra:1308.0026 [pdf] replaced on 2013-09-20 09:07:16

The Structurization of a Set of Positive Integers and Its Application to the Solution of the Twin Primes Problem

Authors: Alexander Fedorov
Comments: 25 Pages.

One of causes why Twin Primes problem was unsolved over a long period is that pairs of Twin Primes (PTP) are considered separately from other pairs of Twin Numbers (PTN). By purpose of this work is research of connections between different types of PTN. For realization of this purpose by author was developed the "Arithmetic of pairs of Twin Numbers" (APTN). In APTN are defined three types PTN. As shown in APTN all types PTN are connected with each other by relations which represent distribution of prime and composite positive integers less than n between them. On the basis of this relations (axioms APTN) are deduced formulas for computation of the number of PTN (NPTN) for each types. In APTN also is defined and computed Average value of the number of pairs are formed from odd prime and composite positive integers $ < n $ . Separately AVNPP for prime and AVNPC for composite positive integers. We also deduced formulas for computation of deviation NPTN from AVNPP and AVNPC. It was shown that if $n$ go to infinity then NPTN go to AVNPC or AVNPP respectively that permit to apply formulas for AVNPP and AVNPC to computation of NPTN. At the end is produced the proof of the Twin Primes problem with help of APTN. It is shown that if n go to infinity then NPTP go to infinity.
Category: Number Theory

[1] viXra:1308.0007 [pdf] submitted on 2013-08-01 17:50:20

A Formula that Generates a Type of Pairs of Poulet Numbers

Authors: Marius Coman
Comments: 2 Pages.

Starting from the observation that the number 13^2 + 81*13 + 3*13*41 is a Poulet number (2821), and the number 41^2 + 81*41 + 3*13*41 is a Poulet number too (6601), and following my interest for the number 30, I found a formula that generates such pairs of Poulet numbers like (2821,6601).
Category: Number Theory