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 and it's 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 2 exactly. In other words, twin primes is a pair of two prime numbers which have the prime gap of 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 valid proof/disproof for twin prime conjecture since roughly more than 170 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).

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).

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 ◽  
Thermal Physics ◽  
Twin Primes ◽  
Detailed Explanation ◽  
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 pajir”. 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).

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 The Nicholson's conjecture

2021 ◽  
Author(s):  
Jan Feliksiak
Keyword(s):  
Research Paper ◽  
Prime Numbers ◽  
Point Of View ◽  
The Difference ◽  
Prime Gaps

This research paper discusses the distribution of prime numbers, from the point of view of the Nicholson's conjecture of 2013. The proof of the conjecture, permits to develop and establish a Supremum bound, on the difference of terms of the conjecture. Nicholson's conjecture belongs to the class of the strongest bounds on maximal prime gaps.

scholarly journals A Metacognitive MOOC Framework

2019 ◽  
pp. 234-250
Author(s):  
Jennifer Roberts ◽  
Ignatius Gous
Keyword(s):  
Service Quality ◽  
Research Paper ◽  
Content Delivery ◽  
Completion Rate ◽  
Measurement Scale ◽  
Completion Rates ◽  
The Difference ◽  
Learner’S Perspective

MOOC completion rates are well documented as being very low, in most cases, between 5% to 15% (Greene, Oswald, Pomerantz, 2015; Jordan, 2014). Many reasons have been suggested for the low completion rate. This paper investigates the thesis that one of the predictors of the low completion rates, is that students are not satisfied with the overall experience (structure, content, delivery, etc.) of the MOOC. According to the SERVQUAL measurement scale of satisfaction, service quality can be defined as the difference between expectations and actual experiences. The argument put forward in this paper is that service quality will be enhanced if students’ expectation of the MOOC is well understood and that they are properly prepared for what to expect when undertaking the MOOC. This paper follows from an already accepted research paper featuring an auto ethnographic journey of undertaking a MOOC. The author proposed a metacognitive MOOC framework, from a learner’s perspective, based on her MOOC journey. In this paper, this metacognitive MOOC framework is examined in terms of reflective as well as practical components, to assist prospective MOOC students to be prepared for the experience and enhance their satisfaction with their MOOC.

Magic squares of squares over a finite field

2021 ◽  
pp. 111-122
Author(s):  
Stewart Hengeveld ◽  
Giancarlo Labruna ◽  
Aihua Li
Keyword(s):  
Finite Field ◽  
Prime Numbers ◽  
Similar Question ◽  
Magic Squares ◽  
Content Type ◽  
Magic Square ◽  
Twin Primes ◽  
Quadratic Residues ◽  
Perfect Squares ◽  
Open Question

A magic square M M over an integral domain D D is a 3 × 3 3\times 3 matrix with entries from D D such that the elements from each row, column, and diagonal add to the same sum. If all the entries in M M are perfect squares in D D , we call M M a magic square of squares over D D . In 1984, Martin LaBar raised an open question: “Is there a magic square of squares over the ring Z \mathbb {Z} of the integers which has all the nine entries distinct?” We approach to answering a similar question when D D is a finite field. We claim that for any odd prime p p , a magic square over Z p \mathbb Z_p can only hold an odd number of distinct entries. Corresponding to LaBar’s question, we show that there are infinitely many prime numbers p p such that, over Z p \mathbb Z_p , magic squares of squares with nine distinct elements exist. In addition, if p ≡ 1 ( mod 120 ) p\equiv 1\pmod {120} , there exist magic squares of squares over Z p \mathbb Z_p that have exactly 3, 5, 7, or 9 distinct entries respectively. We construct magic squares of squares using triples of consecutive quadratic residues derived from twin primes.

scholarly journals III. The sums of the series of the reciprocals of the prime numbers and of their powers

1882 ◽  
Vol 33 (216-219) ◽  
pp. 4-10 ◽  
Keyword(s):  
Prime Numbers ◽  
Natural Numbers ◽  
The Difference

Euler has shown that it is possible to sum the series of reciprocals of powers of the prime numbers, and he has calculated the values of these sums for the even powers. I thought it of some interest to calculate the sums for the odd powers, and to evaluate a peculiar constant (somewhat analogous to the Eulerian constant,— γ = 0·57721 56649 01532 86060 65) which presents itself, in the series of simple reciprocals of primes, as the difference between the sum of the series and the double logarithmic infinity to the Napierian base ϵ. The summation of these series was shown by Euler to depend upon the Napierian logarithms of the sums of the reciprocals of the powers of the natural numbers.

Index, sub-index and sub-factor of groups with interactions to number theory

2019 ◽  
Vol 19 (06) ◽  
pp. 2050101
Author(s):  
M. H. Hooshmand
Keyword(s):  
Number Theory ◽  
Direct Product ◽  
Prime Numbers ◽  
Additive Number Theory ◽  
Open Problems ◽  
Famous Conjecture ◽  
Future Directions ◽  
Left And Right ◽  
The Difference ◽  
Equivalent Conditions

This paper is the first step of a new topic about groups which has close relations and applications to number theory. Considering the factorization of a group into a direct product of two subsets, and since every subgroup is a left and right factor, we observed that the index conception can be generalized for a class of factors. But, thereafter, we found that every subset [Formula: see text] of a group [Formula: see text] has four related sub-indexes: right, left, upper and lower sub-indexes [Formula: see text], [Formula: see text] which agree with the conception index of subgroups, and all of them are equal if [Formula: see text] is a subgroup or normal sub-semigroup of [Formula: see text]. As a result of the topic, we introduce some equivalent conditions to a famous conjecture for prime numbers (“every even number is the difference of two primes”) that one of them is: the prime numbers set is index stable (i.e. all of its sub-indexes are equal) in integers and [Formula: see text]. Index stable groups (i.e. those whose subsets are all index stable) are a challenging subject of the topic with several results and ideas. Regarding the extension of the theory, we give some methods for evaluation of sub-indexes, by using the left and right differences of subsets. At last, we pose many open problems, questions, a proposal for additive number theory, and show some future directions of researches and projects for the theory.

Sign in / Sign up

Export Citation Format

Share Document