[11] **viXra:1902.0406 [pdf]**
*submitted on 2019-02-25 03:49:20*

**Authors:** Dariusz Gołofit

**Comments:** 8 Pages.

If we elimate an ordered subset from the ordered set, we will receive a subset od orderly character.

**Category:** Number Theory

[10] **viXra:1902.0405 [pdf]**
*submitted on 2019-02-25 03:54:25*

**Authors:** Dariusz Gołofit

**Comments:** 12 Pages.

If we elimate an ordered subset from the ordered set, we will receive a subset od orderly character.

**Category:** Number Theory

[9] **viXra:1902.0395 [pdf]**
*submitted on 2019-02-23 20:22:29*

**Authors:** Nicholas R. Wright

**Comments:** 7 Pages.

This proof identifies the three solutions to the three ABC-conjecture formulations. Given that the ABC-conjecture’s relevance to a slew of unsolved problems, other equations will be proven by inspection. Aside from the ABC conjecture, this proof will solve for a hypothetical Moore graph of diameter 2, girth 5, degree 57 and order 3250 (degree-diameter problem); the Collatz conjecture; and the Beal conjecture. Discussion and conclusion will review a unifying solution by spectral graph theory.

**Category:** Number Theory

[8] **viXra:1902.0390 [pdf]**
*replaced on 2019-03-16 21:21:15*

**Authors:** ZhangAik, Leet_Noob

**Comments:** 2 Pages.

The elementary proof to the twin conjecture.

**Category:** Number Theory

[7] **viXra:1902.0235 [pdf]**
*submitted on 2019-02-13 05:23:19*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 6 Pages. Submitted to the The Ramanujan Journal. Comments welcome.

In this paper, we consider the abc conjecture in the case c=a+1. Firstly, we give the proof of the first conjecture that c

**Category:** Number Theory

[6] **viXra:1902.0200 [pdf]**
*submitted on 2019-02-11 06:24:07*

**Authors:** Faisal Amin Yassein Abdelmohssin

**Comments:** 2 Pages.

I claim that the sum of following distinct proper fractions [(1/2),(1/3),(1/6)] is the only triple of distinct proper fraction that sum to 1 {i.e. [(1/2)+(1/3)+(1/6)]=1}.

**Category:** Number Theory

[5] **viXra:1902.0147 [pdf]**
*replaced on 2019-05-03 15:42:36*

**Authors:** Kenneth A. Watanabe

**Comments:** 9 Pages.

The Near-Square Prime conjecture, states that there are an infinite number of prime numbers of the form x^2 + 1. In this paper, a function was derived that determines the number of prime numbers of the form x^2 + 1 that are less than n^2 + 1 for large values of n. Then by mathematical induction, it is proven that as the value of n goes to infinity, the function goes to infinity, thus proving the Near-Square Prime conjecture.

**Category:** Number Theory

[4] **viXra:1902.0106 [pdf]**
*replaced on 2019-02-10 10:53:42*

**Authors:** Algirdas Antano Maknickas

**Comments:** 2 Pages.

This remark gives analytical solution of Last Fermat's Theorem

**Category:** Number Theory

[3] **viXra:1902.0040 [pdf]**
*submitted on 2019-02-02 16:34:38*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 9 Pages. A Complete proof of the abc conjecture using elementary calculus with numerical examples. Submitted to the Ramanujan Journal. Your comments are welcome.

In this paper, we consider the abc conjecture. Firstly, we give a proof of a first conjecture that c

**Category:** Number Theory

[2] **viXra:1902.0036 [pdf]**
*submitted on 2019-02-03 00:15:01*

**Authors:** Simon Plouffe

**Comments:** 10 Pages.

Une famille de formules permettant d'obtenir une suite de longueur arbitraire de nombres premiers. Ces formules sont nettement plus efficaces que celles de Mills ou Wright. Le procédé permet de produire par exemple une suite dont la croissance est double exponentielle mais l'exposant = 101/100.

**Category:** Number Theory

[1] **viXra:1902.0005 [pdf]**
*replaced on 2019-06-04 10:28:14*

**Authors:** James Edwin Rock

**Comments:** 7 Pages.

Let P_n be the n_th prime. For twin primes P_n – P_(n-1) = 2. Let X be the number of (6j –1, 6j+1) pairs in the interval [P_n, P_n^2]. The number of twin primes (TPAn) in [P_n, P_n^2] can be approximated by the formula
(a_3 /5)(a_4 /7)(a_5 /11)…(a_n /P_n)(X) for 3 ≤ m ≤ n, a_m = P_m –2 .
We establish a lower bound for TPAn (3/5)(5/7)(7/9)…(P_n–2)/P_n)(X) = 3X/P_n < TPAn.
We exhibit a formula showing as P_n increases, the number of twin primes in the interval [P_n, P_n^2] also increases. Let P_n – P_(n-1) = c. For all n (TPAn-1)(1+(2c –2)/2P_(n-1)+(c^2–2c)/2P_(n-1)^2) < TPAn

**Category:** Number Theory