A prime pair based interleaver design for IDMA systems

2012 ◽  
Author(s):  
Haibo Peng ◽  
Shouhao Wu ◽  
Jianhua Ji
Keyword(s):  
Prime Pair

PRIME PAIR LABELING OF GRAPHS AND DIGRAPHS

2020 ◽  
Vol 9 (5) ◽  
pp. 2687-2700
Author(s):  
G. Suganya ◽  
K. Palani ◽  
T. M. Velammal
Keyword(s):  
Prime Pair

On a Generalization of the Prime Pair Problem

1957 ◽  
Vol 11 (60) ◽  
pp. 249 ◽  
Author(s):  
Herschel F. Smith
Keyword(s):  
Prime Pair

scholarly journals JUMPING CHAMPIONS AND GAPS BETWEEN CONSECUTIVE PRIMES

2011 ◽  
Vol 07 (06) ◽  
pp. 1413-1421 ◽  
Author(s):  
D. A. GOLDSTON ◽  
A. H. LEDOAN
Keyword(s):  
Empirical Evidence ◽  
Prime Pair

The most common difference that occurs among the consecutive primes less than or equal to x is called a jumping champion. Occasionally there are ties. Therefore there can be more than one jumping champion for a given x. In 1999 Odlyzko, Rubinstein and Wolf provided heuristic and empirical evidence in support of the conjecture that the numbers greater than 1 that are jumping champions are 4 and the primorials 2, 6, 30, 210, 2310,…. As a step toward proving this conjecture they introduced a second weaker conjecture that any fixed prime p divides all sufficiently large jumping champions. In this paper we extend a method of Erdős and Straus from 1980 to prove that the second conjecture follows directly from the prime pair conjecture of Hardy and Littlewood.

scholarly journals On a generalization of the prime pair problem

1957 ◽  
Vol 11 (60) ◽  
pp. 249-249 ◽  
Author(s):  
Herschel F. Smith
Keyword(s):  
Prime Pair

Additively unique sets of prime numbers

2018 ◽  
Vol 14 (10) ◽  
pp. 2757-2765 ◽  
Author(s):  
Noah Lebowitz-Lockard
Keyword(s):  
Multiplicative Function ◽  
Prime Numbers ◽  
Prime Pair ◽  
Identity Function

Spiro proved that the identity function is the only multiplicative function with [Formula: see text] for some prime [Formula: see text] and [Formula: see text] for all prime [Formula: see text] and [Formula: see text]. We determine the sets [Formula: see text] of primes for which restricting our condition to [Formula: see text] for all [Formula: see text] still implies that [Formula: see text] is the identity function. We prove that [Formula: see text] satisfies these conditions if and only if [Formula: see text] contains every prime that is not the larger element of a twin prime pair and [Formula: see text] contains [Formula: see text] or [Formula: see text].

scholarly journals R-prime numbers of degree k

2018 ◽  
Vol 38 (2) ◽  
pp. 75-82
Author(s):  
Abdelhakim Chillali
Keyword(s):  
Number Theory ◽  
Prime Number ◽  
Complexity Theory ◽  
Prime Numbers ◽  
Prime Pair ◽  
Random Input ◽  
Trap Door ◽  
Twin Primes ◽  
Open Questions ◽  
One Way Function

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient of a function for it to be called one-way (see Theoretical Definition, in article). A twin prime is a prime number that has a prime gap of two, in other words, differs from another prime number by two, for example the twin prime pair (5,3). The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture, which states: There are infinitely many primes p such that p + 2 is also prime. In this work we define a new notion: ‘r-prime number of degree k’ and   we give a new RSA trap-door one-way. This notion generalized a twin prime numbers because the twin prime numbers are 2-prime numbers of degree 1.

scholarly journals Disproof of Twin Prime Conjecture

2019 ◽  
Author(s):  
K.H.K. Geerasee Wijesuriya
Keyword(s):  
Research Paper ◽  
Prime Numbers ◽  
Prime Pair ◽  
Twin Primes ◽  
The Difference ◽  
Valid Proof

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

scholarly journals Proof of Twin Prime Conjecture that can be obtained by using Contradiction method in Mathematics

2020 ◽  
Author(s):  
K.H.K. Geerasee Wijesuriya
Keyword(s):  
Research Paper ◽  
Prime Numbers ◽  
Prime Pair ◽  
Twin Primes ◽  
The Difference ◽  
Valid Proof

Twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the part “twin prime” is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid proof for twin prime conjecture.

scholarly journals In detail explanation for the “Proof of the Twin Prime Conjecture” and its applications to thermal physics

2021 ◽  
Author(s):  
K.H.K. Geerasee Wijesuriya
Keyword(s):  
Research Paper ◽  
Prime Numbers ◽  
Prime Pair ◽  
Thermal Physics ◽  
Twin Primes ◽  
The World ◽  
Subject Areas ◽  
The Difference ◽  
Three Space ◽  
Valid Proof

Twin prime numbers are two prime numbers which have the difference equals to exactly 2. In other words, twin primes is a pair of two prime numbers which have the value of the difference exactly two. Sometimes the word “twin prime” is used for a pair of twin primes; an another name for this is considered as “prime twin” or called as “prime pair”. Up to date there is no any exact proof/disproof for twin prime conjecture since roughly 200 years in the world. Through this research paper, my attempt is to provide a valid proof for twin prime conjecture. This new paper is the detailed explanation of my previous paper that I completed on mid of the year 2020 titled as ‘Proof of Twin Prime Conjecture that can be obtained by using Contradiction method in Mathematics’ (WHICH IS WELL-RECONGNIZED ALL OVER THE WORLD through researchgate as well). And this proof of the existence of infinitely many twin primes can be applied to many subject areas in Physics, Chemistry and etc. And the proof of twin prime conjecture can be used to solve several unsolved problems in Physics, Chemistry and etc as well. Also as an additional result, at the end of this research paper, it discusses about an application of the Proof of Twin Prime Conjecture to the Quantum and Thermal Physics. There, this research paper consider three space volumes symbolized as area A , B and C. Inside areas A and B there are microscopic particles separately. By applying the proof of the twin prime conjecture, finally this will try to conclude that although the areas A and B have separated by area C, there are some particles those have moved from the area B to area A (due to the high thermal pressure of area B).

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