Sondow et al have studied Ramanujan primes (RPs) and observed numerically that, while half of all primes are RPs asymptotically, one obtains runs of consecutives RPs (resp. non-RPs) which are statistically significantly longer than one would expect if one was tossing an unbiased coin. In this discussion paper we attempt a heuristic explanation of this phenomenon. Our heuristic follows naturally from the Prime Number Theorem, but seems to be only partly satisfactory. It motivates why one should obtain long runs of both RPs and non-RPs, and also longer runs of non-RPs than of RPs. However, it also suggests that one should obtain longer runs of RPs than have so far been observed in the data, and this issue remains puzzling. NOTE: This is purel...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) ...
In this thesis, we focus on the problem of primes in short intervals. We will explore the main ingre...
Abstract In 1845, Bertrand conjectured that for all integers x ≥ 2, there exists at least one prime ...
In this article, we study the Ramanujan-prime-counting function piR(x) along the lines of Ramanujan’...
A numerical study on the distributions of primes in short intervals of length $h$ over the natural n...
The study into specific properties of the partition function has been a rich topic for number theori...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
Abweichender Titel nach Übersetzung der Verfasserin/des VerfassersPrime numbers have been a signific...
Dedicated to T N Shorey on his sixtieth birthday Abstract. We study some arithmetic properties of th...
The Fundamental Theorem of Arithmetic states that every composite integer can be written as a unique...
It is the purpose of this thesis to enunciate and prove a collection of explicit results in the...
The asymptotic frequency with which pairs of primes below x differ by some fixed integer is understo...
This is an article for a general mathematical audience on the author's work, joint with Terence Tao,...
Abstract The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) ...
In this thesis, we focus on the problem of primes in short intervals. We will explore the main ingre...
Abstract In 1845, Bertrand conjectured that for all integers x ≥ 2, there exists at least one prime ...
In this article, we study the Ramanujan-prime-counting function piR(x) along the lines of Ramanujan’...
A numerical study on the distributions of primes in short intervals of length $h$ over the natural n...
The study into specific properties of the partition function has been a rich topic for number theori...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
Abweichender Titel nach Übersetzung der Verfasserin/des VerfassersPrime numbers have been a signific...
Dedicated to T N Shorey on his sixtieth birthday Abstract. We study some arithmetic properties of th...
The Fundamental Theorem of Arithmetic states that every composite integer can be written as a unique...
It is the purpose of this thesis to enunciate and prove a collection of explicit results in the...
The asymptotic frequency with which pairs of primes below x differ by some fixed integer is understo...
This is an article for a general mathematical audience on the author's work, joint with Terence Tao,...
Abstract The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) ...
In this thesis, we focus on the problem of primes in short intervals. We will explore the main ingre...