On the twin primes (original) (raw)
Related papers
The Twin Primes Conjecture - Some Solutions
viXra, 2012
The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper, which consists of 2 parts that are each self-contained, presents some approaches to the twin primes problem.
The Twin Primes Conjecture - Solutions
2012
The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper, which consists of 5 parts that are each self-contained, presents strong arguments which support the validity of the twin primes conjecture. MSC: 11-XX (Number Theory)
Conjecture of Twin Primes ( Still Unsolved Problem in Number Theory ) an Expository
2018
The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called ”Twin primes conjecture” (8 problem of David Hilbert, stated in 1900) which has eluded many gifted mathematicians. This conjecture has been circulating for decades, even with the progress of contemporary technology that puts the whole world within our reach. So, simple to state, yet so hard to prove. Basic Concepts, many and varied topics regarding the Twin prime conjecture will be cover. Petronas towers (Twin towers) Kuala Lumpur, Malaysia 2010 Mathematics Subject Classification: 11A41; 97Fxx; 11Yxx.
Twin primes: classical results and new developments
2019
While the notion of prime numbers has existed for millennia, twin primes have only been around for little over a century. Although it is not known whether there are infinitely many twin primes, the prime gap was very recently shown to be no greater than 246. The fact that the summed reciprocals of twin primes converge to approximately 1.9 has also been demonstrated. It has further been established that there do exist infinitely many primes p for which p+2 is the product of no more than two primes. A criterion for twin primes does exist but it is neither sufficient to show the existence of an infinite number of them, nor feasible as a computational tool.
Conjecture of twin primes (Still unsolved problem in Number Theory). An expository essay
Surveys in Mathematics and its Applications, 2017
The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called "Twin primes conjecture" (8th problem of David Hilbert, stated in 1900) which has eluded many gifted mathematicians. This conjecture has been circulating for decades, even with the progress of contemporary technology that puts the whole world within our reach. So, simple to state, yet so hard to prove. Basic Concepts, many and varied topics regarding the Twin prime conjecture will be cover.
2016
Euclid’s proof of the infinitude of the primes has generally been regarded as elegant. It is a proof by contradiction, or, reductio ad absurdum, and it relies on an algorithm which will always bring in larger and larger primes, an infinite number of them. However, the proof is also subtle and has been misinterpreted by some with one well-known mathematician even remarking that the algorithm might not work for extremely large numbers. This paper, which is a revision/expansion of the author’s earlier paper published in an international mathematics journal in 2003, presents a strong argument which supports the validity of the twin primes conjecture, using reasoning similar to that of Euclid’s proof of the infinity of the primes. (This paper is published in an international mathematics journal.)
A Simple Argument Supporting Twin Prime Conjectures
viXra, 2015
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.