Number Theory

1301 Submissions

[5] viXra:1301.0195 [pdf] submitted on 2013-01-31 03:09:33

A List of Known Root Prime-Generating Quadratic Polynomials Producing More Than 23 Distinct Primes in a Row

Authors: Marius Coman
Comments: 4 Pages. I discovered myself some of these polynomials and submitted few to OEIS; I know the other ones from the articles available on Internet.

A simple list of known such polynomials, indexed by the value of discriminants, containing no analysis but the introduction of the “root prime generating polynomial” notion.
Category: Number Theory

[4] viXra:1301.0131 [pdf] replaced on 2014-03-15 05:24:07

Fermat's Last Theorem Hanson Boys' Grammar School Proof

Authors: Barry Foster
Comments: 4 Pages.

This is a short proof(?) of Fermat's Last Theorem only using mathematical methods known to boys in a 1950's English grammar school.
Category: Number Theory

[3] viXra:1301.0129 [pdf] replaced on 2013-02-01 09:02:23

Goldbach Conjecture is False

Authors: Liu Ran
Comments: 11 Pages.

This paper has proved Goldbach conjecture is false with set theoryand higher mathematics knowledge. A program on computer is to verifypreliminary theorem. A prediction has become the evidence to verify the finding being true or false.
Category: Number Theory

[2] viXra:1301.0066 [pdf] replaced on 2014-01-27 14:29:03

On Exponential Decay and the Riemann Hypothesis

Authors: Jeffrey N. Cook
Comments: 74 Pages. Fix a couple minor typos.

A Riemann operator is constructed in which sequential elements are removed from a decaying set by means of prime factorization, leading to a form of exponential decay with zero degeneration, referred to as the root of exponential decay. A proportionate operator is then constructed in a similar manner in terms of the non-trivial zeros of the Riemann zeta function, extending proportionately, mapping expectedly always to zero, which imposes a ratio of the primes to said zeta roots. Thirdly, a statistical oscillation function is constructed algebraically into an expression of the Laplace transform that links the two operators and binds the roots of the functions in such a manner that the period of the oscillation is defined (and derived) by the eigenvalues of one and the elements of another. A proof then of the Riemann hypothesis is obtained with a set of algebraic paradoxes that unmanageably occur for the single incident of any non-trivial real part greater or less than a rational one half.
Category: Number Theory

[1] viXra:1301.0021 [pdf] submitted on 2013-01-05 01:53:52

Number Systems Based On Logical Calculus

Authors: Pith Xie
Comments: 22 Pages.

The reference \cite{Ref1} denote number systems with a logical calculus, but the form of natural numbers are not consistently in these number systems. So we rewrite number systems to correct the defect.
Category: Number Theory