Add to ORKGIn this paper, a problem posed in [1] by Smarandache concerning the prime gaps is analyzed. Let's p n be the n-th prime number and d n the following ratio: d n pn+ 1 − pn = where n ≥ 1 2 If we indicate with g n = pn+1 − pn the gap between two consecutive primes, the previous equation becomes: g n d n = 2 In [1], Smarandache posed the following questions: 1. Does the sequence d n contain infinite primes? 2. Analyze the distribution of n d First of all let's observe that d n is a rational number only for n=1, being p 1 = 2, p
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Abstract. Fix an integer g 6 = −1 that is not a perfect square. In 1927, Artin conjectured that ther...
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152784/1/mtks0025579300007567.pd
This paper is concerned with formulation and demonstration of new versions of equations that can hel...
Abstract. A “theoretical ” distribution of prime number gaps is proposed and compared with the actua...
Five conjectures on the gaps between consecutive primes are formulated. One expresses the number of ...
A prime gap is the difference between two successive prime numbers. Two is the smallest possible gap...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...
Let $p_n$ be the $n$th smallest prime and $d_n\defeq p_{n+1}-p_n$ the gap between $p_n$ and $p_{n+1}...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
The paper presents a brief history of results about small gaps between con¬secutive primes and menti...
Abstract. In this note we discuss the primes in Smarandache progressIons. For any positive integer n...
. By a prime gap of size g, we mean that there are primes p and p+g such that the g \Gamma 1 numbers...
In this paper, we investigate a special prime gap problem which results from Dirichlet's theorem and...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Abstract. Fix an integer g 6 = −1 that is not a perfect square. In 1927, Artin conjectured that ther...
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152784/1/mtks0025579300007567.pd
This paper is concerned with formulation and demonstration of new versions of equations that can hel...
Abstract. A “theoretical ” distribution of prime number gaps is proposed and compared with the actua...
Five conjectures on the gaps between consecutive primes are formulated. One expresses the number of ...
A prime gap is the difference between two successive prime numbers. Two is the smallest possible gap...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...
Let $p_n$ be the $n$th smallest prime and $d_n\defeq p_{n+1}-p_n$ the gap between $p_n$ and $p_{n+1}...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
The paper presents a brief history of results about small gaps between con¬secutive primes and menti...
Abstract. In this note we discuss the primes in Smarandache progressIons. For any positive integer n...
. By a prime gap of size g, we mean that there are primes p and p+g such that the g \Gamma 1 numbers...
In this paper, we investigate a special prime gap problem which results from Dirichlet's theorem and...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Abstract. Fix an integer g 6 = −1 that is not a perfect square. In 1927, Artin conjectured that ther...
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152784/1/mtks0025579300007567.pd