ترغب بنشر مسار تعليمي؟ اضغط هنا

A new enlightenment about gaps between primes

158   0   0.0 ( 0 )
 نشر من قبل Samir Brahim Belhaouari
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea of our approach is summarized on the creation and on the analyzing sequence of sets of distinct co-primes with the first $n$ primes, $left{ p_i :, ileq n right}$, and the important properties of the modulus linear combination of the co-prime sets, $H=left(1,p_{n+1},..., Pi_{i=1}^n p_i-1right) $, that gives sets of even numbers ${0,2,4,..., Pi_{i=1}^n p_i -2 }$. Furthermore, by generalizing our approach, the Polignac conjecture the existence of infinitely many cousin primes, $p_{n+1}-p_{n}=4$, and the statement that every even integer can be expressed as a difference of two primes, are derived as well.



قيم البحث

اقرأ أيضاً

148 - Lynn Chua , Soohyun Park , 2014
We use Maynards methods to show that there are bounded gaps between primes in the sequence ${lfloor nalpharfloor}$, where $alpha$ is an irrational number of finite type. In addition, given a superlinear function $f$ satisfying some properties describ ed by Leitmann, we show that for all $m$ there are infinitely many bounded intervals containing $m$ primes and at least one integer of the form $lfloor f(q)rfloor$ with $q$ a positive integer.
Let $t in mathbb{N}$, $eta >0$. Suppose that $x$ is a sufficiently large real number and $q$ is a natural number with $q leq x^{5/12-eta}$, $q$ not a multiple of the conductor of the exceptional character $chi^*$ (if it exists). Suppose further that, [ max {p : p | q } < exp (frac{log x}{C log log x}) ; ; {and} ; ; prod_{p | q} p < x^{delta}, ] where $C$ and $delta$ are suitable positive constants depending on $t$ and $eta$. Let $a in mathbb{Z}$, $(a,q)=1$ and [ mathcal{A} = {n in (x/2, x]: n equiv a pmod{q} } . ] We prove that there are primes $p_1 < p_2 < ... < p_t$ in $mathcal{A}$ with [ p_t - p_1 ll qt exp (frac{40 t}{9-20 theta}) . ] Here $theta = (log q) / log x$.
We present in this work a heuristic expression for the density of prime numbers. Our expression leads to results which possesses approximately the same precision of the Riemanns function in the domain that goes from 2 to 1010 at least. Instead of usi ng a constant as was done by Legendre and others in the formula of Gauss, we try to adjust the data through a function. This function has the remarkable property: its points of discontinuity are the prime numbers.
340 - Abiya Rajans , G. Ambika 2020
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the connections among the nodes are made based on the divisibility pattern among the numbers. We derive analytical expressions for the centrality measures of this network in terms of the floor function and the divisor functions. We validate these measures with the help of standard methods which make use of the adjacency matrix of the network. Thus how the measures of the network relate to patterns in the behaviour of primes and composite numbers becomes apparent from our study.
106 - Chunlei Liu 2021
It is proven that there are infinitely prime pairs whose difference is no greater than 20.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا