[16] **viXra:1303.0195 [pdf]**
*replaced on 2014-08-16 05:17:11*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Generalization of Lucas-Lehmer-Riesel primality test is introduced .

**Category:** Number Theory

[15] **viXra:1303.0191 [pdf]**
*replaced on 2014-07-19 13:39:42*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Generalizations of Wilson's theorem and Kilford's theorem are introduced .

**Category:** Number Theory

[14] **viXra:1303.0190 [pdf]**
*replaced on 2014-08-12 06:52:14*

**Authors:** Predrag Terzic

**Comments:** 3 Pages.

Prime number generating recurrences are introduced .

**Category:** Number Theory

[13] **viXra:1303.0183 [pdf]**
*submitted on 2013-03-24 04:26:14*

**Authors:** Keith Hodebourg

**Comments:** 15 Pages.

On the particular distribution of prime numbers is a case to be treated in several parts. In the
first place, I will treat the prime identity Δ, which is the method that allows one to discern
with certainty prime numbers γ, of strong non-prime numbers ω, and non-prime numbers μ,
amongst the series of natural wholes A, as in :.....................

**Category:** Number Theory

[12] **viXra:1303.0182 [pdf]**
*submitted on 2013-03-24 04:28:16*

**Authors:** Keith Hodebourg

**Comments:** 01 Pages.

The german mathematician Christian Goldbach, in a letter dated 1742 to Leonhard Euler,
announced a conjecture which affirm that any even number greater than or equal to 4 is the
sum of two prime numbers........................

**Category:** Number Theory

[11] **viXra:1303.0181 [pdf]**
*submitted on 2013-03-24 04:30:33*

**Authors:** Keith Hodebourg

**Comments:** 01 Pages.

In 1937 the Swedish mathematician Harald Cramer put forth the hypothesis that there always
exists a prime number between X and X (InX)2, I respons in this way :..............

**Category:** Number Theory

[10] **viXra:1303.0180 [pdf]**
*submitted on 2013-03-24 04:33:02*

**Authors:** Keith Hodebourg

**Comments:** 01 Pages.

The twin prime numbers conjecture announces the hypothesis that there exists an infinite of
twin prime numbers, I respond in this way :.........

**Category:** Number Theory

[9] **viXra:1303.0135 [pdf]**
*submitted on 2013-03-19 02:43:19*

**Authors:** Marius Coman

**Comments:** 5 Pages.

Though the method of concatenation has it’s recognised place in number theory, is rarely leading to the determination of characteristics of an entire class of numbers, which is not defined only through concatenation. We present here a property related to concatenation that appears to be shared by a large subset of Carmichael numbers.

**Category:** Number Theory

[8] **viXra:1303.0113 [pdf]**
*submitted on 2013-03-15 09:39:12*

**Authors:** M. MADANI Bouabdallah

**Comments:** 07 Pages. French language

The set of (6n - 1,6n +1)is an abelian group for n rational integer.

**Category:** Number Theory

[7] **viXra:1303.0109 [pdf]**
*submitted on 2013-03-14 17:52:41*

**Authors:** Edigles Bezerra Guedes

**Comments:** 7 pages

We discovery some formulas for the divisor function, derived from a Vinogradov’s formula and definitions these function, including the Ramanujan’s sum. As well, we have developed a formula asymptotic, using the Euler-Maclaurin summation formula.

**Category:** Number Theory

[6] **viXra:1303.0088 [pdf]**
*submitted on 2013-03-12 03:24:32*

**Authors:** Chun-Xuan Jiang

**Comments:** 413 Pages.

1.Foudations of Santilli isonumber theory.I:isonumber theory of the first kind;2.Santilli isonumber theory.II:isonumber theory of the second kind;3.Fermat last theorem and its applications;4.the proofs of binary Goldbach theorem using only partial primes;5.Santilli isocryptographic theory.Disproofs of Riemann hypothesis.

**Category:** Number Theory

[5] **viXra:1303.0081 [pdf]**
*submitted on 2013-03-11 07:14:43*

**Authors:** Marius Coman

**Comments:** 4 Pages.

Though they are a fascinating class of numbers, there are very many properties of Carmichael numbers still unstudied enough. I have always thought there is a connection between these numbers and the sum of their digits (few of them are also Harshad numbers). I try here to highlight such a possible connection.

**Category:** Number Theory

[4] **viXra:1303.0048 [pdf]**
*submitted on 2013-03-07 11:32:32*

**Authors:** Edigles Bezerra Guedes

**Comments:** 6 pages

We prove the Legendre’s conjecture: given an integer, n>0, there is always one prime, p, such that n^2<p<(n+1)^2, using the prime-counting function and the Bertrand’s Postulate.

**Category:** Number Theory

[3] **viXra:1303.0047 [pdf]**
*submitted on 2013-03-07 11:35:37*

**Authors:** Edigles Bezerra Guedes

**Comments:** 7 pages

We prove the Oppermann’s conjecture: given an integer, n>1, there is, at least, one prime between n^2-n and n^2, and, at least, another prime between n^2 and n^2+n, using the prime-counting function and the Bertrand’s Postulate.

**Category:** Number Theory

[2] **viXra:1303.0031 [pdf]**
*submitted on 2013-03-06 04:31:54*

**Authors:** Marius Coman

**Comments:** 6 Pages.

Despite the development of computer systems, the chains of succesive primes obtained through an iterative formula yet have short lenghts; for instance, the largest known chain of primes in arithmetic progression is an AP-26. We present here few formulas that might lead to interesting chains of primes.

**Category:** Number Theory

[1] **viXra:1303.0019 [pdf]**
*submitted on 2013-03-04 08:27:01*

**Authors:** Nikolay Dementev

**Comments:** 4 Pages.

Algorithm for determining whether given number is a prime or a composite is conjectured. The algorithm implies neither division operation, nor the counting to more than two to be an a priori knowledge.

**Category:** Number Theory