Related papers: On three consecutive primes
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
We prove explicit bounds for the number of sums of consecutive prime squares below a given magnitude.
In this note we prove an inequality involving primes and the product of consecutive primes.
In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.
For earlier considered our sequence A166944 in [4] we prove three statements of its connection with twin primes. We also give a sufficient condition for the infinity of twin primes and pose several new conjectures; among them we propose a…
In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins
We present a new, elementary, dynamical proof of the prime number theorem.
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
We give an explicit form of Ingham's Theorem on primes in the short intervals, and show that there is at least one prime between every two consecutive cubes $x\sp{3}$ and $(x+1)\sp{3}$ if $\log\log x\ge 15$.
This version of the paper corrects an inaccuracy in the proof of Theorem 2.9 in the published version. The main results remain unchanged.
The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.
We survey the classical results on the prime number theorem
I give some claims on primorial prime numbers for interested readers in number theory.
We proved that there are infinitely many cousin primes.
In the recent article arXiv:1606.03351, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the end they…
We prove several congruences for trinomial coefficients.
Vinogradov's three primes theorem indicates that, for every sufficiently large odd integer $N$, the equation $N=p_1+p_2+p_3$ is solvable in prime variables $p_1,p_2,p_3$. In this paper, it is proved that Vinogradov's three primes theorem…
In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.
We introduce extremely symmetric primes and provide some elementary properties of these.