Number Theory

1511 Submissions

[9] viXra:1511.0270 [pdf] submitted on 2015-11-28 06:51:19

Generic Form of the Poulet Numbers Having a Prime Factor of the Form 30n+23

Authors: Marius Coman
Comments: 2 Pages.

In this paper I observe that many Poulet numbers P having a prime factor q of the form 30*n + 23, where n positive integer, can be written as P = m*(q^2 – q) + q^2, where m positive integer, and I conjecture that any Poulet number P having 23 as a prime factor can be written as P = 506*m + 529, where m positive integer.
Category: Number Theory

[8] viXra:1511.0229 [pdf] submitted on 2015-11-23 22:19:44

Conjecture on the Numbers of the Form Np^2-Np+p-2 Where P Prime

Authors: Marius Coman
Comments: 2 Pages.

In this paper I conjecture that there exist, for any p prime, p greater than or equal to 7, an infinity of positive integers n such that the number n*p^2 – n*p + p – 2 is prime.
Category: Number Theory

[7] viXra:1511.0227 [pdf] replaced on 2015-11-23 22:21:31

A Note on the Wilson's Theorem

Authors: Hitesh Jain
Comments: 5 Pages.

We obtained two interesting congruence relations related to Wilson’s theorem.
Category: Number Theory

[6] viXra:1511.0226 [pdf] replaced on 2015-11-27 05:22:41

Generalized Riemann Hypothesis and Why Doctors Get It Wrong About When You Will Die

Authors: David Brown
Comments: 3 Pages.

According to the Clay Mathematics Institute, “The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2.” Furthermore, if you can write out a valid mathematical proof of the Riemann hypothesis and get it published in a refereed mathematical journal then the Clay Mathematics Institute will, after due deliberation, give you a prize of one million U.S. dollars. The Riemann hypothesis has a generalization to Dirichlet L-functions, among others. What might the Riemann hypothesis and medical predictions have in common? Experience suggests that both are difficult. It might be that accurate prediction of outcomes is mathematically and empirically intractable in almost all interesting cases. Stephen Wolfram’s Principle of Computational Equivalence states that “Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication.” This brief communication offers two conjectures concerning the generalized Riemann hypothesis for Dirichlet L-functions. In addition to medical doctors and number theory, this brief communication makes reference to Abraham Lincoln and a set of dogs with cardinality one.
Category: Number Theory

[5] viXra:1511.0218 [pdf] submitted on 2015-11-23 03:45:24

A Simple Argument Supporting Twin Prime Conjectures

Authors: Dhananjay P. Mehendale
Comments: 4 pages.

Prime numbers are infinite since the time when Euclid gave his one of the most beautiful proof of this fact! Prime number theorem (PNT) reestablishes this fact and further it also gives estimate about the count of primes less than or equal to x. PNT states that as x tends to infinity the count of primes up to x tends to x divided by the natural logarithm of x. Twin primes are those primes p for which p+2 is also a prime number. The well known twin prime conjecture (TPC) states that twin primes are (also) infinite. Related to twin primes further conjectures that can be made by extending the thought along the line of TPC, are as follows: Prime numbers p for which p+2n is also prime are (also) infinite for all n, where n = 1(TPC), 2, 3, …, k, …. In this paper we provide a simple argument in support of all twin prime conjectures.
Category: Number Theory

[4] viXra:1511.0193 [pdf] submitted on 2015-11-20 10:44:03

On Composites and Primes

Authors: Safaa Moallim
Comments: 10 Pages.

In this paper, I introduce two concepts, first is number influence strength, and second is count of influenced multiples less than x. going from there, we can calculate how many composites is less than x stepping to how many primes is less than x.
Category: Number Theory

[3] viXra:1511.0140 [pdf] submitted on 2015-11-16 23:08:46

Proof Prime Due to Square Number is an Infinite

Authors: Hajime Mashima
Comments: 1 Page.

Prime number is infinite. This proof is similar to the Euclid's theorem(300 B.C.).
Category: Number Theory

[2] viXra:1511.0102 [pdf] replaced on 2016-03-15 01:10:58

On Generalized Harmonic Numbers, Tornheim Double Series and Linear Euler Sums

Authors: Kunle Adegoke
Comments: 44 Pages. Corrected typos, added theorems

Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a linear combination of Tornheim double series of the same weight. New closed form evaluations of various Euler sums are presented. Finally certain combinations of linear Euler sums that are reducible to Riemann zeta values are discovered.
Category: Number Theory

[1] viXra:1511.0031 [pdf] submitted on 2015-11-03 11:56:46

Natural Neutrosophic Numbers and MOD Neutrosophic Numbers

Authors: W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache
Comments: 188 Pages.

The authors in this book introduce a new class of natural neutrsophic numbers using MOD intervals. These natural MOD neutrosophic numbers behave in a different way for the product of two natural neutrosophic numbers can be neutrosophic zero divisors or idempotents or nilpotents. Several open problems are suggested in this book.
Category: Number Theory