**Previous months:**

2007 - 0703(3) - 0706(2)

2008 - 0807(1) - 0809(1) - 0810(1) - 0812(2)

2009 - 0901(2) - 0904(2) - 0907(2) - 0908(4) - 0909(1) - 0910(2) - 0911(1) - 0912(3)

2010 - 1001(3) - 1002(1) - 1003(55) - 1004(50) - 1005(36) - 1006(7) - 1007(11) - 1008(16) - 1009(21) - 1010(8) - 1011(7) - 1012(13)

2011 - 1101(14) - 1102(7) - 1103(13) - 1104(3) - 1105(1) - 1106(2) - 1107(1) - 1108(2) - 1109(3) - 1110(5) - 1111(4) - 1112(4)

2012 - 1201(2) - 1202(13) - 1203(7) - 1204(9) - 1205(7) - 1206(6) - 1207(5) - 1208(5) - 1209(11) - 1210(15) - 1211(10) - 1212(4)

2013 - 1301(5) - 1302(10) - 1303(16) - 1304(15) - 1305(12) - 1306(13) - 1307(26) - 1308(12) - 1309(9) - 1310(13) - 1311(16) - 1312(21)

2014 - 1401(20) - 1402(11) - 1403(25) - 1404(12) - 1405(19) - 1406(21) - 1407(35) - 1408(52) - 1409(1)

Any replacements are listed further down

[757] **viXra:1409.0003 [pdf]**
*submitted on 2014-09-01 10:02:24*

**Authors:** Liu Ran

**Comments:** 1 Page.

传统数论中的无穷大是没有上界的，也就是没有最大，只有更大。无穷大是自相矛盾的。

**Category:** Number Theory

[756] **viXra:1408.0231 [pdf]**
*submitted on 2014-08-31 12:01:39*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 13*2^n+1 is introduced .

**Category:** Number Theory

[755] **viXra:1408.0230 [pdf]**
*submitted on 2014-08-31 12:10:44*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time compositeness tests for numbers of the form k10^n-c and k10^n+c are introduced .

**Category:** Number Theory

[754] **viXra:1408.0225 [pdf]**
*submitted on 2014-08-31 00:12:58*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make four conjectures on primes, conjectures which involve the sums of distinct unit fractions such as 1/p(1) + 1/p(2) + (...), where p(1), p(2), (...) are distinct primes, more specifically the periods of the rational numbers which are the results of the sums mentioned above.

**Category:** Number Theory

[753] **viXra:1408.0223 [pdf]**
*submitted on 2014-08-31 01:36:10*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I present three formulas, each of them with the following property: starting from a given prime p, are obtained in many cases two other primes, q and r. I met the triplets of primes [p, q, r] obtained with these formulas in the study of Carmichael numbers; the three primes mentioned are often the three prime factors of a 3-Carmichael number.

**Category:** Number Theory

[752] **viXra:1408.0221 [pdf]**
*submitted on 2014-08-31 06:11:45*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture which states that any prime greater than or equal to 53 can be written at least in one way as a sum of three odd primes, not necessarily distinct, of the same form from the following four ones: 10k + 1, 10k + 3, 10k + 7 or 10k + 9.

**Category:** Number Theory

[751] **viXra:1408.0220 [pdf]**
*submitted on 2014-08-31 06:41:55*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture which states that any square of a prime greater than or equal to 7 can be written at least in one way as a sum of three odd primes, not necessarily distinct, but all three of the form 10k + 3 or all three of the form 10k + 7.

**Category:** Number Theory

[750] **viXra:1408.0218 [pdf]**
*submitted on 2014-08-30 12:33:04*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 7*2^n+1 is introduced .

**Category:** Number Theory

[749] **viXra:1408.0217 [pdf]**
*submitted on 2014-08-30 12:34:57*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 11*2^n+1 is introduced .

**Category:** Number Theory

[748] **viXra:1408.0212 [pdf]**
*submitted on 2014-08-29 14:54:03*

**Authors:** Stephen Marshall

**Comments:** 11 Pages.

This paper presents a complete and exhaustive proof of the infinitude of Mersenne prime numbers. The approach to this proof uses same logic that Euclid used to prove there are an infinite number of prime numbers. Then we prove that if p > 1 and d > 0 are integers, that p and p + d are both primes if and only if for integer n (see reference 1 and 2):
n=(p-1)!(1/p+(-1)dd!/(p + d))+1/p+ 1/(p+d)
We use this proof for d = 2p(k+m) - 2p(k) to prove the infinitude of Mersenne prime numbers.

**Category:** Number Theory

[747] **viXra:1408.0210 [pdf]**
*submitted on 2014-08-29 11:21:12*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I present a formula for generating big primes and products of very few primes, based on the numbers 25 and 906304, formula equally extremely interesting and extremely simple, id est 25^n + 906304. This formula produces for n from 1 to 30 (and for n = 30 is obtained a number p with not less than 42 digits) only primes or products of maximum four prime factors.

**Category:** Number Theory

[746] **viXra:1408.0209 [pdf]**
*submitted on 2014-08-29 12:10:30*

**Authors:** Stephen Marshall

**Comments:** 6 Pages.

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 29 is a Sophie Germain prime because it is a prime and 2 × 29 + 1 = 59, and 59 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain. We shall prove that there are an infinite number of Sophie Germain primes.

**Category:** Number Theory

[745] **viXra:1408.0208 [pdf]**
*submitted on 2014-08-29 07:28:09*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 5*2^n+1 is introduced .

**Category:** Number Theory

[744] **viXra:1408.0201 [pdf]**
*submitted on 2014-08-28 15:30:00*

**Authors:** Stephen Marshall

**Comments:** 12 Pages.

This paper presents a complete and exhaustive proof that an Infinite Number of Triplet Primes exist. The approach to this proof uses same logic that Euclid used to prove there are an
infinite number of prime numbers. Then we prove that if p > 1 and d > 0 are integers, that p and p + d are both primes if and only if for integer n (see reference 1 and 2):
n =(p−1)!(1/p+(−1)d(d!)/(p + d)+ 1/(p+1)+ 1/(p+d)
We use this proof and Euclid logic to prove only an infinite number of Triplet Primes exist. However we shall begin by assuming that a finite number of Triplet Primes exist, we shall
prove a contradiction to the assumption of a finite number, which will prove that
an infinite number of Triplet Primes exist.

**Category:** Number Theory

[743] **viXra:1408.0197 [pdf]**
*submitted on 2014-08-28 12:50:19*

**Authors:** Anibal Fernando Barral

**Comments:** 24 Pages.

In mathematics, a prime number is a natural number that is divisible only by 1 and itself.
For centuries, the search for an algorithm that could generate the sequence of these numbers became a mystery.
Perhaps the problem arises at the beginning of the enterprise, that is, the search for a single algorithm.
I noticed that all the primes without exception increased by one unit in some cases, or decreased by one unit in the other cases result in a multiple of 6 (six)
Example: 5+1=6 ; 7-1=6 ; 11+1=12 ; 13-1=12 ; 17+1=18 ; 19-1=18 ; 23+1=24 ; 29+1=30 ; 31-1=30 ;
37-1=36 ; 41+1=42 ; 43-1=42 ; 47+1=48 ; and so on.
Then I thought of making it easier to split the problem solving both cases.
So are passed to assume the presence of # 2 complementary families of primes.
To the number 1000, I worked by hand, a job with some effort but great satisfaction.
At this point my algorithms were reliable, but I needed another test.
To get to number 60,000 I leaned in a computational program, which compiled a dear friend. I would have liked to get up to 1,000,000 but the limit of 60,000 has been imposed by the processing time of the data.
At this point I had no more doubts about the reliability of my algorithms that are developed in continuation.

**Category:** Number Theory

[742] **viXra:1408.0195 [pdf]**
*submitted on 2014-08-28 08:44:01*

**Authors:** Matthias Lesch

**Comments:** 3 Pages.

In recent three preprints S. Marshall claims to give proofs of several famous conjectures in number theory, among them the twin prime conjecture and Goldbach's conjecture. A claimed proof of Beal's conjecture would even imply an elementary proof of Fermat's Last Theorem.
It is the purpose of this note to point out serious errors. It is the opinion of this author that it is safe to say that the claims of the above mentioned papers are lacking any basis.

**Category:** Number Theory

[741] **viXra:1408.0193 [pdf]**
*submitted on 2014-08-27 18:59:21*

**Authors:** Simon Plouffe

**Comments:** 38 Pages.

I present here a collection of algorithms that permits the expansion into a finite series or sequence from a real number x∈ R, the precision used is 64 decimal digits. The collection of mathematical constants was taken from my own collection and theses sources [1]-[6][9][10]. The goal of this experiment is to find a closed form of the sequence generated by the algorithm. Some new results are presented.

**Category:** Number Theory

[740] **viXra:1408.0190 [pdf]**
*submitted on 2014-08-27 23:33:11*

**Authors:** Francis Thasayyan

**Comments:** 3 Pages.

This document gives an answer to Beal's Conjection.

**Category:** Number Theory

[739] **viXra:1408.0189 [pdf]**
*submitted on 2014-08-28 00:37:39*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 9*2^n+1 is introduced .

**Category:** Number Theory

[738] **viXra:1408.0184 [pdf]**
*submitted on 2014-08-27 09:13:25*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of numbers of the form k6^n-1 is introduced .

**Category:** Number Theory

[737] **viXra:1408.0183 [pdf]**
*submitted on 2014-08-27 05:41:21*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of numbers of the form kb^n-1 is introduced .

**Category:** Number Theory

[736] **viXra:1408.0181 [pdf]**
*submitted on 2014-08-26 22:22:43*

**Authors:** Simon Plouffe

**Comments:** 9 Pages. The abstract in english and the main text in french

The iteration formula Z_(n+1)=Z_n^2+c of Mandelbrot will give an algebraic number of degree 4 when it converges most of the time. If we take a good look at some of these algebraic numbers: some of them have a very persistent pattern in their binary expansion.
La formule d’itération de Mandelbrot Z_(n+1)=Z_n^2+c converge vers un nombre algébrique de degré 4 si c est un rationnel simple. Mais en regardant de près certains nombres algébriques en binaire on voit apparaître un motif assez évident et très persistant.

**Category:** Number Theory

[735] **viXra:1408.0180 [pdf]**
*submitted on 2014-08-26 22:24:59*

**Authors:** Simon Plouffe

**Comments:** 13 Pages. The abstract in english and the main text in french

An analysis of the function 1/π Arg ζ((1/2)+in) is presented. This analysis permits to find a general expression for that function using elementary functions of floor and fractional part. These formulas bring light to a remark from Freeman Dyson which relates the values of the ζfunction to quasi-crystals. We find these same values for another function which is very similar, namely 1/π Arg Γ((1/4)+in/2). These 2 sets of formula have a definite pattern, the n’th term is related to values like π,ln(π),ln(2),…,log(p), where p is a prime number. The coefficients are closed related to a certain sequence of numbers which counts the number of 0’s from the right in the binary representation of n. These approximations are regular enough to deduce an asymptotic and precise formula. All results presented here are empirical.

**Category:** Number Theory

[734] **viXra:1408.0176 [pdf]**
*submitted on 2014-08-26 07:18:46*

**Authors:** Ramón Ruiz

**Comments:** 34 Pages. This research is based on an approach developed solely to demonstrate the binary Goldbach Conjecture and the Twin Primes Conjecture.

Goldbach's Conjecture statement: “Every even integer greater than 2 can be expressed as the sum of two primes”.
Initially, to prove this conjecture, we can form two arithmetic sequences (A and B) different for each even number, with all the natural numbers that can be primes, that can added, in pairs, result in the corresponding even number.
By analyzing the pairing process, in general, between all non-prime numbers of sequence A, with terms of sequence B, or vice versa, to obtain the even number, we note that some pairs of primes are always formed. This allow us to develop a non-probabilistic formula, to calculate the approximate number of pairs of primes that meet the conjecture for an even number x.
The result of this formula is always equal or greater than 1, and it tends to infinite when x tends to infinite, which allow us to confirm that Goldbach's Conjecture is true.
The prime numbers theorem by Carl Friedrich Gauss, the prime numbers theorem in arithmetic progressions and some axioms have been used to complete this investigation.

**Category:** Number Theory

[733] **viXra:1408.0175 [pdf]**
*submitted on 2014-08-26 07:27:11*

**Authors:** Ramón Ruiz

**Comments:** 24 Pages. This research is based on an approach developed solely to demonstrate the Twin Primes Conjecture and the binary Goldbach Conjecture.

Twin Primes Conjecture statement: “There are infinitely many primes p such that (p + 2) is also prime”.
Initially, to prove this conjecture, we can form two arithmetic sequences (A and B), with all the natural numbers, lesser than a number x, that can be primes and being each term of sequence B equal to its partner of sequence A plus 2.
By analyzing the pairing process, in general, between all non-prime numbers of sequence A, with terms of sequence B, or vice versa, we note that some pairs of primes are always formed. This allow us to develop a non-probabilistic formula to calculate the approximate number of pairs of primes, p and (p + 2), that are lesser than x.
The result of this formula tends to infinite when x tends to infinite, which allow us to confirm that the Twin Primes Conjecture is true.
The prime numbers theorem by Carl Friedrich Gauss, the prime numbers theorem in arithmetic progressions and some axioms have been used to complete this investigation.

**Category:** Number Theory

[732] **viXra:1408.0174 [pdf]**
*submitted on 2014-08-26 08:02:11*

**Authors:** Stephen Marshall

**Comments:** 10 Pages.

This paper presents a complete and exhaustive proof of the Polignac Prime Conjecture. The approach to this proof uses same logic that Euclid used to prove there are an infinite number of prime numbers. Then we prove that if p > 1 and d > 0 are integers, that p and p+ d are both primes if and only if for integer n (see reference 1 and 2):
n =(p−1)!(1/p+(−1)d(d!)/(p + d)+ 1/(p+1)+ 1/(p+d)
We use this proof for d = 2k to prove the infinitude of Polignac prime numbers.
Additionally, our proof of the Polignac Prime Conjecture leads to proofs of several other significant number theory conjectures such as the Goldbach Conjecture, Twin Prime Conjecture, Cousin Prime Conjecture, and Sexy Prime Conjecture. Our proof of Polignac’s Prime Conjecture provides significant accomplishments to Number Theory, yielding proofs to several conjectures in number theory that has gone unproven for hundreds of years.

**Category:** Number Theory

[731] **viXra:1408.0173 [pdf]**
*submitted on 2014-08-26 08:10:03*

**Authors:** Stephen Marshall

**Comments:** 7 Pages.

Abstract: This paper presents a complete and exhaustive proof of the Beal Conjecture. The approach to this proof uses the Fundamental Theorem of Arithmetic as the basis for the proof of the Beal Conjecture. The Fundamental Theorem of Arithmetic states that every number greater than 1 is either prime itself or is unique product of prime numbers. The prime factorization of every number greater than 1 is used throughout every section of the proof of the Beal Conjecture. Without the Fundamental Theorem of Arithmetic, this approach to proving the Beal Conjecture would not be possible.

**Category:** Number Theory

[730] **viXra:1408.0169 [pdf]**
*submitted on 2014-08-25 18:53:30*

**Authors:** Stephen Marshall

**Comments:** 8 Pages.

This paper presents a complete and exhaustive proof of the Fibonacci Prime Conjecture. The approach to this proof uses same logic that Euclid used to prove there are an infinite number of prime numbers. Then we prove that if p > 1 and d > 0 are integers, that p and p+ d are both primes if and only if for integer n (see reference 1 and 2):
n =(p−1)!(1/p+(−1)d(d!)/(p + d)+ 1/(p+1)+ 1/(p+d)
We use this proof for p = Fy-1 and d = Fy-2 to prove the infinitude of Fibonacci prime numbers.

**Category:** Number Theory

[729] **viXra:1408.0166 [pdf]**
*submitted on 2014-08-25 09:29:06*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 3*2^n+1 is introduced .

**Category:** Number Theory

[728] **viXra:1408.0150 [pdf]**
*submitted on 2014-08-23 02:35:15*

**Authors:** Barry Foster

**Comments:** 2 Pages.

This attempt does not require knowledge of the distribution of primes.

**Category:** Number Theory

[727] **viXra:1408.0134 [pdf]**
*submitted on 2014-08-20 08:04:44*

**Authors:** Predrag Terzic

**Comments:** 4 Pages.

Conjectured polynomial time primality and compositeness tests for numbers of special forms are introduced .

**Category:** Number Theory

[726] **viXra:1408.0128 [pdf]**
*submitted on 2014-08-19 05:07:11*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

We use the positivity axiom of inner product spaces to prove the equivalent statement of the Riemann hypothesis.

**Category:** Number Theory

[725] **viXra:1408.0126 [pdf]**
*submitted on 2014-08-18 15:16:53*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time primality tests for specific classes of numbers of the form kb^n-1 are introduced .

**Category:** Number Theory

[724] **viXra:1408.0119 [pdf]**
*submitted on 2014-08-18 09:49:52*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time primality test for specific class of numbers of the form 9b^n-1 is introduced .

**Category:** Number Theory

[723] **viXra:1408.0113 [pdf]**
*submitted on 2014-08-18 06:11:05*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make five conjectures about the primes r, t and the square of prime p^2, which appears as solutions in the diophantine equation 120*n*q*r + 1 = p^2, where n is non-null positive integer.

**Category:** Number Theory

[722] **viXra:1408.0111 [pdf]**
*submitted on 2014-08-18 02:11:31*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make two conjectures abut the pairs of primes [p1, q1], where the difference between p1 and q1 is a certain even number d. I state that any such pair has at least one other corresponding, in a specified manner, pair of primes [p2, q2], such that the difference between p2 and q2 is also equal to d.

**Category:** Number Theory

[721] **viXra:1408.0110 [pdf]**
*submitted on 2014-08-18 00:02:36*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture which states that any odd prime can be written in a certain way, in other words that any such prime can be expressed using just another prime and the powers of the numbers 2, 3 and 5. I also make a related conjecture about twin primes.

**Category:** Number Theory

[720] **viXra:1408.0098 [pdf]**
*submitted on 2014-08-16 08:37:00*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Compositeness criteria for specific classes of numbers of the form b^n+b+1 and b^n-b-1 are introduced .

**Category:** Number Theory

[719] **viXra:1408.0095 [pdf]**
*submitted on 2014-08-16 05:39:21*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time primality test for specific class of numbers of the form 3b^n-1 is introduced .

**Category:** Number Theory

[718] **viXra:1408.0087 [pdf]**
*submitted on 2014-08-14 07:34:55*

**Authors:** William Maclachlan

**Comments:** 11 Pages.

The aim of my "experiment" was to gather some curious information about the understanding of primes- to my understanding I seemed to have created a system that can find primes considerably quicker in contrast to merely searching through all the given number's factors.
I am not a professional, but it would be nice if I could get some form of a reply from someone with experience to explain the irrelevancy of my findings.

**Category:** Number Theory

[717] **viXra:1408.0085 [pdf]**
*submitted on 2014-08-14 03:16:30*

**Authors:** Pingyuan Zhou

**Comments:** 5 Pages. Author gives an argument for the infinity of primes of the form 2x^2-1 by the infinity of near-square primes of Mersenne primes to arise from a corresponding Fermat prime criterion.

Abstract: In this paper we consider primes of the form 2x^2-1 and discover there is a very great probability for appearing of such primes, and give an argument for the infinity of primes of the form 2x^2-1 by the infinity of near-square primes of Mersenne primes.

**Category:** Number Theory

[716] **viXra:1408.0083 [pdf]**
*submitted on 2014-08-14 00:17:08*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of numbers of the form k6^n-1 is introduced .

**Category:** Number Theory

[715] **viXra:1408.0079 [pdf]**
*submitted on 2014-08-13 07:26:37*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time compositeness tests for numbers of the form k2^n-c and k2^n+c are introduced .

**Category:** Number Theory

[714] **viXra:1408.0071 [pdf]**
*submitted on 2014-08-12 02:52:56*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of generalized Fermat numbers is introduced .

**Category:** Number Theory

[713] **viXra:1408.0068 [pdf]**
*submitted on 2014-08-11 10:15:02*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time compositeness tests for numbers of the form k2^n-1 and k2^n+1 are introduced .

**Category:** Number Theory

[712] **viXra:1408.0050 [pdf]**
*submitted on 2014-08-08 18:22:49*

**Authors:** Oh Jung Uk

**Comments:** 20 Pages. I don't know how to show abstract well

If π_g (N) is the number of cases that even number N could be expressed as the sum of the two primes of 6n±1 type then the formula of π_g (N) is below
π_g (6n+0)=n-1- 2/3 ∑_(k=1)^(n-1)▒((〖πβ〗_g (6k-1))/(πβ_g (6k-1)-1)) -2/3π ∑_(k=1)^(n-1)▒∑_(m=1)^∞▒sin((2〖mπ〗^2 β_g (6k-1))/(πβ_g (6k-1)-1))/m
where,β_g (6k-1)=τ(6k-1)-2+τ(6(n-k)+1)-2,…
But,the formula of π_g (6n+2),π_g (6n-2) is omitted in abstract.

**Category:** Number Theory

[711] **viXra:1408.0046 [pdf]**
*submitted on 2014-08-08 08:35:19*

**Authors:** Th. Guyer

**Comments:** 1 Page.

A briefly olympic idea about P = NP
(include the Prime_Twin_Conjecture)
Whoever is able to(o) kicks out m(e?

**Category:** Number Theory

[710] **viXra:1408.0044 [pdf]**
*submitted on 2014-08-08 04:07:06*

**Authors:** Oh Jung Uk

**Comments:** 21 Pages. I don't know how to show abstract well

If π_t (6n+1) is the number of twin prime of 6n+1 or less then the formula of π_t (6n+1) is described below.
π_t (6n+1)=n+1-2/3 ∑_(k=1)^n▒((πβ_t (6k))/(πβ_t (6k)-1)) -2/3π ∑_(k=1)^n▒∑_(m=1)^∞▒sin((2〖mπ〗^2 β_t (6k))/(πβ_t (6k)-1))/m
where,β_t (6k)={τ(6k-1)-2}+{τ(6k+1)-2},…

**Category:** Number Theory

[709] **viXra:1408.0043 [pdf]**
*submitted on 2014-08-08 04:11:24*

**Authors:** Oh Jung Uk

**Comments:** 16 Pages. I don't know how to show abstract well

For Mersenne prime of 2^(6n+1)-1 type, if a Mersenne prime is 2^(6p+1)-1, just next Mersenne prime is 2^(6x+1)-1 then the following equation is satisfied.
x =p+3/2+1/2 ∑_(k=p+1)^x▒〖(πβ(2^(6k+1)-1)+1)/(πβ(2^(6k+1)-1)-1)+1/π ∑_(k=p+1)^x▒∑_(m=1)^∞▒sin((2mπ^2 β(2^(6k+1)-1))/(πβ(2^(6k+1)-1)-1))/m〗
where,β(2^(6k+1)-1)=τ(2^(6k+1)-1)-2,…
Mersenne prime of 2^(6n-1)-1 type is omitted in abstract.

**Category:** Number Theory

[708] **viXra:1408.0042 [pdf]**
*submitted on 2014-08-08 04:16:18*

**Authors:** Oh Jung Uk

**Comments:** 12 Pages. I don't know how to show abstract well

A number of 6n-1 type is not odd perfect number, Fermat number is not also odd perfect number.
And, if Fermat number is composite number then Fermat number is factorized as below
when n is odd number,2^(2^n )+1=(2^(n+1) (3k+1)+1)(2^(n+1) (3m)+1)
when n is even number,2^(2^n )+1=(2^(n+1) ((3k+1)/2)+1)(2^(n+1) (3m)+1)
And, all Fermat number for n≥5 is composite number.

**Category:** Number Theory

[707] **viXra:1408.0041 [pdf]**
*submitted on 2014-08-07 22:23:12*

**Authors:** Oh Jung Uk

**Comments:** 34 Pages. I don't know how I can fix the abstract

The formula of prime-counting function π(N=6n+3) is described below.
π(N=6n+3)=2n+2-2/3 ∑_(k=1)^n▒{πβ(6k-1)/(πβ(6k-1)-1)+πβ(6k+1)/(πβ(6k+1)-1)} -2/3π ∑_(k=1)^n▒∑_(m=1)^∞▒{(sin((2mπ^2 β(6k-1))/(πβ(6k-1)-1))+sin((2mπ^2 β(6k+1))/(πβ(6k+1)-1)))/m}
where,β(6k-1)=τ(6k-1)-2,β(6k+1)=τ(6k+1)-2,…

**Category:** Number Theory

[706] **viXra:1408.0003 [pdf]**
*submitted on 2014-08-02 01:48:13*

**Authors:** Russell Letkeman

**Comments:** 4 Pages.

We study the spacings of numbers co-prime to an even consecutive product of primes, P_m\# and its structure exposed by the fundamental theorem of prime sieving (FTPS). We extend this to prove some parts of the Hardy-Littlewood general prime density conjecture for all finite multiplicative groups modulo a primorial. We then use the FTPS to prove such groups have gap spacings which form arithmetic progressions as long as we wish. We also establish their densities and provide prescriptions to find them.

**Category:** Number Theory

[705] **viXra:1408.0001 [pdf]**
*submitted on 2014-08-01 05:16:54*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make two conjectures, one about how could be expressed a prime of the form 6k + 1 and one about how could be expressed a prime of the form 6k – 1.

**Category:** Number Theory

[704] **viXra:1407.0224 [pdf]**
*submitted on 2014-07-30 20:04:10*

**Authors:** Russell Letkeman

**Comments:** 3 Pages.

We build a simple recursive model for the prime numbers which at its heart is the prime sieve of Eratosthenes. We also show for prime numbers greater than 3 and their gaps posses a handedness which forbids a large range of possibilities for the choice of intervals in arithmetic progressions.

**Category:** Number Theory

[703] **viXra:1407.0214 [pdf]**
*submitted on 2014-07-29 23:15:32*

**Authors:** Russell Letkeman

**Comments:** 7 Pages.

We show every set modulo the product of a random collection of unique prime numbers has a palindrome in its gaps of length the minimum set minus 1. There is one more gap which is always a twin. Together the count of the gaps equals the count of the minimum modular set. This symmetry not only forces all constellations of gaps to have mirror images existing at exactly the same counts, but it also precisely identifies the center of mass (counts) of the set.

**Category:** Number Theory

[702] **viXra:1407.0209 [pdf]**
*submitted on 2014-07-29 02:38:15*

**Authors:** Pingyuan Zhou

**Comments:** 9 Pages. Author gives an argument for indirect connections between Fermat primes and regular 2^k-sided polygons to make Gauss-Wantzel theorem have general sense in implying connections between Fermat primes and all constructible polygons.

Abstract: Gauss-Wantzel theorem shows that regular n-sided polygons, whose number of sides contains a(distrinct) Fermat prime(s) as odd prime factor(s) of n or number of sides is power of 2, are all constructible with compass and straightedge. But of these caces, the constructibility of all regular 2^k-sided polygons is not related to Fermat primes. We discover the number of so-called root Mersenne primes Mp for p

**Category:** Number Theory

[701] **viXra:1407.0205 [pdf]**
*submitted on 2014-07-27 17:21:20*

**Authors:** JinHua Fei

**Comments:** 7 Pages.

In this paper, we assume that weaker Hardy-Littlewood Conjecture, we got a better upper bound of the exceptional real zero for a class of prime number module.

**Category:** Number Theory

[700] **viXra:1407.0203 [pdf]**
*submitted on 2014-07-27 20:37:59*

**Authors:** Réjean Labrie

**Comments:** 7 Pages.

This article is a demonstration of the existence of at least one prime number between two consecutive squares.

**Category:** Number Theory

[699] **viXra:1407.0201 [pdf]**
*submitted on 2014-07-27 03:06:26*

**Authors:** T.Nakashima

**Comments:** 1 Page.

This Paper is the result Counting the Prime Numbers by using Mathematica 9.

**Category:** Number Theory

[698] **viXra:1407.0166 [pdf]**
*submitted on 2014-07-21 18:58:13*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 7 Pages.

The critical line lies on a surface. And the critical line inherits the characteristics from this surface. Then, the location of the critical line can be determined.

**Category:** Number Theory

[697] **viXra:1407.0164 [pdf]**
*submitted on 2014-07-22 01:26:41*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I present two possible infinite sequences of primes, having in common the fact that their formulas contain the powers of the number 2.

**Category:** Number Theory

[696] **viXra:1407.0159 [pdf]**
*submitted on 2014-07-21 04:04:27*

**Authors:** Marius Coman

**Comments:** 1 Page.

In this paper I make a conjecture which states that any prime greater than or equal to 5 can be written in a certain way, in other words that any such prime can be expressed using just two other primes and a power of the number 2.

**Category:** Number Theory

[695] **viXra:1407.0158 [pdf]**
*submitted on 2014-07-21 04:47:52*

**Authors:** Marius Coman

**Comments:** 3 Pages.

These conjectures state that any prime p greater than 60 can be written as a sum of three primes of a certain type from the following four ones: 10k + 1, 10k + 3, 10k + 7 and 10k + 9.

**Category:** Number Theory

[694] **viXra:1407.0157 [pdf]**
*submitted on 2014-07-21 05:43:31*

**Authors:** Marius Coman

**Comments:** 1 Page.

In this paper I present two possible infinite sequences of primes, having in common the fact that their formulas contain the number 360.

**Category:** Number Theory

[693] **viXra:1407.0153 [pdf]**
*submitted on 2014-07-20 23:20:01*

**Authors:** Pingyuan Zhou

**Comments:** 14 Pages. Author presents the strong finiteness of double Mersenne primes and the infinity of root Mersenne primes and near-square primes of Mersenne primes by generalizing conjecture about primality of Mersenne number.

Abstract: In this paper we present the strong finiteness of double Mersenne primes to be a subset of Mersenne primes, the infinity of so-called root Mersenne primes to be also a subset of Mersenne primes and the infinity of so-called near-square primes of Mersenne primes by generalizing our previous conjecture about primality of Mersenne number. These results and our previous results about the strong finiteness of Fermat, double Fermat and Catalan-type Fermat primes [1] give an elementary but complete understanding for the infinity or the strong finiteness of some prime number sequences of the form 2^x±1, which all have a corresponding original continuous natural ( prime ) number sequence. It is interesting that the generalization to near-square primes of Mersenne primes Wp=2(Mp)^2-1 has brought us positive result.

**Category:** Number Theory

[692] **viXra:1407.0152 [pdf]**
*submitted on 2014-07-21 02:26:52*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper are stated ten conjectures on primes, more precisely on the infinity of some types of triplets and quadruplets of primes, all of them using the multiples of the number 30 and also all of them met on the study of Carmichael numbers.

**Category:** Number Theory

[691] **viXra:1407.0151 [pdf]**
*submitted on 2014-07-21 02:50:07*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Prime number sieve using LCM function is introduced .

**Category:** Number Theory

[690] **viXra:1407.0150 [pdf]**
*submitted on 2014-07-21 03:00:29*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper are stated six conjectures on primes, more precisely on the infinity of some types of pairs of primes, all of them met in the study of 3-Carmichael numbers.

**Category:** Number Theory

[689] **viXra:1407.0143 [pdf]**
*submitted on 2014-07-19 16:20:26*

**Authors:** Isaac Mor

**Comments:** 3 Pages.

Odd Perfect Number = 36k+9
In 1953, Jacques Touchard proved that an odd perfect number must be of the form 12k + 1 or 36k + 9.
(Judy A. Holdener discovered a simpler proof of the theorem of Touchard in 2002)
if I am right then I (isaac mor lol) just showed that an odd perfect number must be of the form 36k+9 (19 july 2014)

**Category:** Number Theory

[688] **viXra:1407.0129 [pdf]**
*submitted on 2014-07-17 21:54:39*

**Authors:** Pingyuan Zhou

**Comments:** 9 Pages. In this paper, author presents the strong finiteness of Fermat primes, double Fermat primes and Catalan-type Fermat primes by generalizing previous conjecture about primality of Fermat numbers to double Fermat and Catalan-type Fermat numbers.

Abstract: In this paper we present that so-called double Fermat numbers are an infinite subset of well-known Fermat numbers and so-called Catalan-type Fermat numbers are also an infinite subset of Fermat numbers as well as double Fermat primes and Catalan-type Fermat primes are all strongly finite as Fermat primes do. From it we get the same result that composite Fermat numbers, composite double Fermat numbers and composite Catalan-type Fermat numbers are all infinite.

**Category:** Number Theory

[687] **viXra:1407.0128 [pdf]**
*submitted on 2014-07-17 13:03:45*

**Authors:** Yilun Shang

**Comments:** 5 Pages.

In this note, we consider some generalizations of the Lucas
sequence, which essentially extend sequences to triangular arrays.
Some new and elegant results are derived.

**Category:** Number Theory

[686] **viXra:1407.0117 [pdf]**
*submitted on 2014-07-15 22:13:12*

**Authors:** Pingyuan Zhou

**Comments:** 4 Pages. Aothor presents a near-sguare number sequence of all Mersenne primes, which seems to be an accptable awy in searching for larger primes by known Mersenne primes themselves than the largest known Mersenne prime M57885161.

Abstract: In this paper we present a conjecture that there is a near-square prime number sequence of Mersenne primes to arise from the near-square number sequence Wp=2(Mp)^2-1 generated from all Mersenne primes Mp, in which every term is larger prime number than corresponding perfect number. The conjecture has been verified for the first few prime terms in the near-square prime number sequence and we may expect appearing of near-square prime numbers of some known Mersenne primes with large p-values will become larger primes to be searched than the largest known Mersenne prime M57885161.

**Category:** Number Theory

[685] **viXra:1407.0111 [pdf]**
*submitted on 2014-07-15 06:26:38*

**Authors:** Choe Ryong Gil

**Comments:** 8 pages, two tables

In this paper we introduce a new function, which would be called a sigma-index of the natural
number, and consider its boundedness. This estimate is effective for the Robin inequality.

**Category:** Number Theory

[684] **viXra:1407.0098 [pdf]**
*submitted on 2014-07-14 05:42:42*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I enunciate five conjectures on primes, based on the study of Fermat pseudoprimes and on the author’s believe in the importance of multiples of 30 in the study of primes.

**Category:** Number Theory

[683] **viXra:1407.0096 [pdf]**
*submitted on 2014-07-14 02:57:45*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I enunciate nine conjectures on primes, all of them on the infinity of certain sequences of primes.

**Category:** Number Theory

[682] **viXra:1407.0095 [pdf]**
*submitted on 2014-07-13 12:16:35*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture on the squares of primes of the form 6k + 1, conjecture that states that by a certain deconcatenation of those numbers (each one in other two numbers) it will be obtained similar results.

**Category:** Number Theory

[681] **viXra:1407.0093 [pdf]**
*submitted on 2014-07-13 04:24:29*

**Authors:** Pingyuan Zhou

**Comments:** 4 Pages. Author presents a new and equivalent statement of Fermat's little theorem for Fermat numbers by using double Fermat number formula to give a very simple explanation for all composite Fermat numbers to be pseudoprimes.

Abstract: In this paper we present a new and equivalent statement of Fermat's little theorem for Fermat numbers by introducing double Fermat number formula and give a very simple and accptable explanation for all composite Fermat numbers to be pseudoprimes.

**Category:** Number Theory

[680] **viXra:1407.0083 [pdf]**
*submitted on 2014-07-12 02:11:36*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture on the squares of primes of the form 6k – 1, conjecture that states that by a certain deconcatenation of those numbers (each one in other two numbers) it will be obtained similar results.

**Category:** Number Theory

[679] **viXra:1407.0081 [pdf]**
*submitted on 2014-07-11 03:55:10*

**Authors:** Pingyuan Zhou

**Comments:** 8 Pages. Author presents two symmetric conjectures related to Mersenne and Fermat primes themselves. It may imply that Mersenne primes are infinite but Fermat primes are finite.

Abstract: From existence of the intersection of the set of Mersenne primes and the set of Fermat primes being a set to contain only one element 3 to be the first Mersenne prime and also the first Fermat prime we fell there are connections between Mersenne and Fermat primes. In this paper, it is presented that two symmetric conjectures related to Mersenne and Fermat primes themselves will lead us to expect Mersenne primes to be infinite but Fermat primes to be finite.

**Category:** Number Theory

[678] **viXra:1407.0080 [pdf]**
*submitted on 2014-07-11 05:52:35*

**Authors:** Jinhua Fei

**Comments:** 9 Pages.

This paper use Nevanlinna's Second Main Theorem of the value distribution theory, we got an important conclusion by Riemann hypothesis.Thus, we launch a contradiction.

**Category:** Number Theory

[677] **viXra:1407.0077 [pdf]**
*submitted on 2014-07-11 03:03:25*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I will define four sequences of numbers obtained through concatenation, definitions which also use the notion of “sum of the digits of a number”, sequences that have the property to produce many primes, semiprimes and products of very few prime factors.

**Category:** Number Theory

[676] **viXra:1407.0061 [pdf]**
*submitted on 2014-07-08 13:20:13*

**Authors:** Carlos Giraldo Ospina

**Comments:** 19 Pages.

En este documento se demuestra la existencia de ciclo único para el Algoritmo de Collatz, con ello la conjetura correspondiente queda en firme; de otra parte, sin necesidad de demostrar la existencia de ciclo único, se puede emplear la inducción completa mediante el Teorema de Wailly.

El presente es un documento de lectura lenta y atenta, no significa que sea difícil… en ABCdatos aparecen archivos preliminares acerca del Algoritmo y Conjetura de Collatz; los referidos documentos, criticables en algún aspecto y subsanables con la demostración de ciclo único, son el andamiaje que hizo posible la demostración de la Conjetura de Collatz… plasman aciertos y errores normales en el terreno investigativo… además, muestran las innumerables bellezas del algoritmo… ellos quedarán como legado en la Historia de las Matemáticas…

¡Bienvenido a la ansiada demostración de la Conjetura de Collatz!

[675] **viXra:1407.0057 [pdf]**
*submitted on 2014-07-08 04:15:50*

**Authors:** Dhananjay P. Mehendale

**Comments:** 7 pages

Goldbach conjecture asserts that every even integer greater than 4 is sum of two odd primes. Stated in a letter to Leonard Euler by Christian Goldbach in 1842, this is still an enduring unsolved problem. In this paper we develop a new simple strategy to settle this most easy to state problem which has baffled mathematical community for so long. We show that the existence of two odd primes for every even number greater than 4 to express it as their sum follows from the well known Chinese remainder theorem. We further develop a method to actually determine a pair of primes for any given even number to express it as their sum using remainders modulo all primes up to square root of that given even number.

**Category:** Number Theory

[674] **viXra:1407.0056 [pdf]**
*submitted on 2014-07-07 22:15:58*

**Authors:** Taekyyon Park, Yeonsoo Kim, Jong Min Lee

**Comments:** 10 Pages. To prove Goldbach's conjecture, we developed our own dynamic model for Goldbach partition. This is the first step of our study.

There have been various approach to prove Goldbach's conjecture using analytical number theory. We go back to the starting point of this famous probelm and are able to show that the number of Goldbach partition is related to that of ordered pairs of non-primes. This proof is based on the world's first dynamic model of primes and can be a key to identify the structure of prime numbers.

**Category:** Number Theory

[673] **viXra:1407.0045 [pdf]**
*submitted on 2014-07-05 22:49:54*

**Authors:** Pingyuan Zhou

**Comments:** 9 Pages. Author presents a conjecture called the simple Mersenne conjecture, which may imply there are no more double Mersenne primes.

Abstract: In this paper we conjecture that there is no Mersenne number M(p)=2^p-1 to be prime for p=2^k±1,±3 when k>7, where p is positive integer and k is natural number. It is called the simple Mersenne conjecture and holds till p≤30402457 from status of this conjecture. If the conjecture is true then there are no more double Mersenne primes besides known double Mersenne primes MM(2), MM(3), MM(5), MM(7).

**Category:** Number Theory

[672] **viXra:1407.0031 [pdf]**
*submitted on 2014-07-03 22:53:13*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I present a very simple formula which conducts often to primes or composites with very few prime factors; for instance, for the first 27 consecutive values introduced as “input” in this formula were obtained 10 primes, 4 squares of primes and 12 semiprimes; just 2 from the numbers obtained have three prime factors; but the most interesting thing is that the composites obtained have a special property that make them form a class of numbers themselves.

**Category:** Number Theory

[671] **viXra:1407.0028 [pdf]**
*submitted on 2014-07-03 11:56:14*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In a previous paper I made a generalization of de Polignac’s conjecture. In this paper I extend that generalization as much as is possible.

**Category:** Number Theory

[670] **viXra:1407.0026 [pdf]**
*submitted on 2014-07-03 09:09:42*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I show a set of Poulet numbers, each one of them having the same interesting relation between its prime factors, and I make four conjectures, one about the infinity of this set, one about the infinity of a certain type of duplets respectively triplets respectively quadruplets and so on of primes and finally two generalizations, of the twin primes conjecture respectively of de Polignac’s conjecture.

**Category:** Number Theory

[669] **viXra:1406.0182 [pdf]**
*submitted on 2014-06-30 01:00:00*

**Authors:** Pingyuan Zhou

**Comments:** 5 Pages. Auther presents a conjecture related to distribution of a kind of special prime factors of Fermat numbers, which may imply existence of infinitely many primes of the form x^2+1.

It is well known that there are infinitely many prime factors of Fermat numbers, because prime factor of a Fermat prime is the Fermat prime itself but a composite Fermat number has at least two prime factors and Fermat numbers are pairwise relatively prime. Hence we conjecture that there is at least one prime factor (k^(1/2)*2^(a/2))^2+1 of Fermat number for F(n)-1≤a<F(n+1)-1 (n=0,1,2,3,…), where k^(1/2)is odd posotive integer, a is even positive integer and F(n) is Fermat number. The conjecture holds till a<F(4+1)-1=4294967296 from known evidences. Two corollaries of the conjecture imply existence of infinitely many primes of the form x^2+1, which is one of four basic problems about primes mentioned by Landau at ICM 1912.

**Category:** Number Theory

[668] **viXra:1406.0181 [pdf]**
*submitted on 2014-06-30 02:05:49*

**Authors:** Pingyuan Zhou

**Comments:** 13 Pages. Author presents a conjecture on composite terms in so-called generilized Catalan-Mersenne number sequence, and tries to find a new way to imply existence of infinitely many composite Mersenne numbers whose exponets are primes.

We conjecture that there is at least one composite term in sequence generated from Mersenne-type recurrence relations. Hence we may expect that all terms are composite besides the first few continuous prime terms in Catalan-Mersenne number sequence and composite Mersenne numbers with exponets restricted to prime values are infinite.

**Category:** Number Theory

[667] **viXra:1406.0161 [pdf]**
*submitted on 2014-06-25 16:47:07*

**Authors:** Isaac Mor

**Comments:** 3 Pages. I got rid of the power of p when n=P*Q^2 with a simple proof

if n is an Odd Perfect Number then n=P*Q^2
I got rid of the power of P with a simple proof

**Category:** Number Theory

[666] **viXra:1406.0155 [pdf]**
*submitted on 2014-06-25 09:04:18*

**Authors:** Arnaud Dhallewyn

**Comments:** 5 Pages. Tout droit réservé

Différente démonstration du postulat de Bertrand

**Category:** Number Theory

[325] **viXra:1408.0166 [pdf]**
*replaced on 2014-08-27 05:29:01*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 3*2^n+1 is introduced .

**Category:** Number Theory

[324] **viXra:1408.0166 [pdf]**
*replaced on 2014-08-25 12:25:49*

**Authors:** Predrag Terzic

**Comments:** 1 Page.

Conjectured polynomial time primality test for specific class of 3*2^n+1 is introduced .

**Category:** Number Theory

[323] **viXra:1408.0150 [pdf]**
*replaced on 2014-08-25 12:50:35*

**Authors:** Barry Foster

**Comments:** 2 Pages.

This attempt does not require knowledge of the distribution of primes.

**Category:** Number Theory

[322] **viXra:1408.0134 [pdf]**
*replaced on 2014-08-27 05:27:43*

**Authors:** Predrag Terzic

**Comments:** 4 Pages.

Conjectured polynomial time primality and compositeness tests for numbers of special forms are introduced .

**Category:** Number Theory

[321] **viXra:1408.0126 [pdf]**
*replaced on 2014-08-27 05:23:44*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time primality tests for specific classes of numbers of the form kb^n-1 are introduced .

**Category:** Number Theory

[320] **viXra:1408.0113 [pdf]**
*replaced on 2014-08-18 06:42:15*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make five conjectures about the primes q, r and the square of prime p^2, which appears as solutions in the diophantine equation 120*n*q*r + 1 = p^2, where n is non-null positive integer.

**Category:** Number Theory

[319] **viXra:1408.0068 [pdf]**
*replaced on 2014-08-12 06:36:01*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Conjectured polynomial time compositeness tests for numbers of the form k2^n-1 and k2^n+1 are introduced .

**Category:** Number Theory

[318] **viXra:1407.0214 [pdf]**
*replaced on 2014-07-31 22:10:45*

**Authors:** Russell Letkeman

**Comments:** 6 Pages.

We introduce a fundamental theorem of prime sieving (FTPS) and show how it illuminates structure on numbers co-prime to a random product of unique prime numbers. This theorem operates on the transition between the set of numbers co-prime to any product of unique prime numbers and the new set when another prime number is introduced in the product.

**Category:** Number Theory

[317] **viXra:1407.0166 [pdf]**
*replaced on 2014-07-27 13:08:59*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 7 Pages.

The critical line lies on a surface. And the critical line inherits the characteristics from this surface. Then, the location of the critical line can be determined.

**Category:** Number Theory

[316] **viXra:1407.0083 [pdf]**
*replaced on 2014-07-13 10:45:58*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture on the squares of primes of the form 6k – 1, conjecture that states that by a certain deconcatenation of those numbers (each one in other two numbers) it will be obtained similar results.

**Category:** Number Theory

[315] **viXra:1407.0057 [pdf]**
*replaced on 2014-08-18 03:52:29*

**Authors:** Dhananjay P. Mehendale

**Comments:** 9 pages.

Goldbach conjecture asserts that every even integer greater than 4 is sum of two odd primes. Stated in a letter to Leonard Euler by Christian Goldbach in 1842, this is still an enduring unsolved problem. In this paper we develop a new simple strategy to settle this most easy to state problem which has baffled mathematical community for so long. We show that the existence of two odd primes for every even number greater than 4 to express it as their sum follows from the well known Chinese remainder theorem. We develop a method to actually determine a pair (and subsequently all pairs) of primes for any given even number to express it as their sum. For proof sake we will be using an easy equivalent of Goldbach conjecture. This easy equivalent leads to a congruence system and existence of solution for this congruence system is assured by Chinese remainder theorem. Each such solution actually provides a pair of primes to express given even number as their sum. We also discuss how twin prime conjecture follows from existence of certain x as a solution of certain congruence system.

**Category:** Number Theory

[314] **viXra:1407.0057 [pdf]**
*replaced on 2014-07-17 12:56:15*

**Authors:** Dhananjay P. Mehendale

**Comments:** 8 pages.

Goldbach conjecture asserts that every even integer greater than 4 is sum of two odd primes. Stated in a letter to Leonard Euler by Christian Goldbach in 1842, this is still an enduring unsolved problem. In this paper we develop a new simple strategy to settle this most easy to state problem which has baffled mathematical community for so long. We show that the existence of two odd primes for every even number greater than 4 to express it as their sum follows from the well known Chinese remainder theorem. We develop a method to actually determine a pair (and subsequently all pairs) of primes for any given even number to express it as their sum. For proof sake we will be using an easy equivalent of Goldbach conjecture. This easy equivalent leads to a congruence system and existence of solution for this congruence system is assured by Chinese remainder theorem. Each such solution actually provides a pair of primes to express given even number as their sum.

**Category:** Number Theory

[313] **viXra:1407.0056 [pdf]**
*replaced on 2014-08-07 00:42:10*

**Authors:** Taekyoon park, Yeonsoo Kim, Jong Min Lee

**Comments:** 10 Pages. To prove Goldbach's conjecture, we developed our own dynamic model for Goldbach partition. This is the first step of our study.

There have been various approach to prove Goldbach's conjecture using analytical number theory. We go back to the starting point of this famous probelm and are able to show that the number of Goldbach partition is related to that of ordered pairs of non-primes. This proof is based on the world's first dynamic model of primes and can be a key to identify the structure of prime numbers.

**Category:** Number Theory

[312] **viXra:1407.0056 [pdf]**
*replaced on 2014-08-05 21:50:18*

**Authors:** Taekyoon park, Yeonsoo Kim, Jong Min Lee

**Comments:** 10 Pages. To prove Goldbach's conjecture, we developed our own dynamic model for Goldbach partition. This is the first step of our study.

There have been various approach to prove Goldbach's conjecture using analytical number theory. We go back to the starting point of this famous probelm and are able to show that the number of Goldbach partition is related to that of ordered pairs of non-primes. This proof is based on the world's first dynamic model of primes and can be a key to identify the structure of prime numbers.

**Category:** Number Theory

[311] **viXra:1407.0026 [pdf]**
*replaced on 2014-07-03 12:54:29*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I show a set of Poulet numbers, each one of them having the same interesting relation between its prime factors, and I make four conjectures, one about the infinity of this set, one about the infinity of a certain type of duplets respectively triplets respectively quadruplets and so on of primes and finally two generalizations, of the twin primes conjecture respectively of de Polignac’s conjecture.

**Category:** Number Theory