Add to ORKGWe prove a generalization of the author's work to show that any subset of the primes which is 'well distributed' in arithmetic progressions contains many primes which are close together. Moreover, our bounds hold with some uniformity in the parameters. As applications, we show there are infinitely many intervals of length containing primes, and show lower bounds of the correct order of magnitude for the number of strings of congruent primes with
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
AbstractIn this paper, we consider the sequence 11, + 11 + 22, 11 + 22 + 33, ... and prove some of i...
We prove a generalization of the author's work to show that any subset of the primes which is 'well ...
We introduce a method for showing that there exist prime numbers which are very close together. The ...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
International audienceAbstract We generalize current known distribution results on Shanks–Rényi prim...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Goldston, Pintz and Yıldırım have shown that if the primes have ‘level of distribution’ θ for some θ...
In the current application of our parallelization concept we are using an algorithm involving sievin...
Knowledge about number theory and prime numbersEuclid proved that the number of prime numbers is inf...
AbstractIf A is a dense subset of the integers, then A+A+A contains long arithmetic progressions. Th...
In this paper, we consider the sequence 11, + 11 + 22, 11 + 22 + 33, ... and prove some of its congr...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
The fundamental theorem of arithmetic states that any composite natural integer can be expressed in ...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
AbstractIn this paper, we consider the sequence 11, + 11 + 22, 11 + 22 + 33, ... and prove some of i...
We prove a generalization of the author's work to show that any subset of the primes which is 'well ...
We introduce a method for showing that there exist prime numbers which are very close together. The ...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
International audienceAbstract We generalize current known distribution results on Shanks–Rényi prim...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Goldston, Pintz and Yıldırım have shown that if the primes have ‘level of distribution’ θ for some θ...
In the current application of our parallelization concept we are using an algorithm involving sievin...
Knowledge about number theory and prime numbersEuclid proved that the number of prime numbers is inf...
AbstractIf A is a dense subset of the integers, then A+A+A contains long arithmetic progressions. Th...
In this paper, we consider the sequence 11, + 11 + 22, 11 + 22 + 33, ... and prove some of its congr...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
The fundamental theorem of arithmetic states that any composite natural integer can be expressed in ...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
AbstractIn this paper, we consider the sequence 11, + 11 + 22, 11 + 22 + 33, ... and prove some of i...