Add to ORKGLet G(X) denote the size of the largest gap between consecutive primes below X. Answering a question of Erdős, we show that $G(X)\geqslant f(X)\frac{logX log logX log log log log X}{(log log logX)^2}$, where f(X) is a function tending to infinity with X. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes
Let pn denote the n-th prime. We prove that max/pn+1 ≤ X (pn+1 - pn) ≫ log X log log X log log log l...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...
ABSTRACT. Let G(X) denote the size of the largest gap between consecutive primes below X. Answering ...
AbstractLetG(X) denote the largest gap between consecutive primes belowX. Improving earlier results ...
We show that there exist pairs of consecutive primes less than x whose difference is larger than t(1...
Let pn denote the n-th prime, and for any k > 1 and sufficiently large X , define the quantity Gk...
AbstractLet G(x;q,a):=maxPn⩽x(Pn+1−Pn),Pn‵Pn+1‵amodq where (a, q) = 1 and Pn, Pn + 1 are consecutive...
Abstract. Let n be a natural number. If the sum of the proper divisors of n is less than n, then n i...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
Let q > r ≥ 1 be coprime integers. Let P c = P c ( q , r , H ) be an ...
Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes ...
We show that the existence of arithmetic progressions with few primes, with a quantitative bound on ...
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving...
For a positive integer $n$, we denote by $F(n)$ the distance from $n$ to the nearest prime number. W...
Let pn denote the n-th prime. We prove that max/pn+1 ≤ X (pn+1 - pn) ≫ log X log log X log log log l...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...
ABSTRACT. Let G(X) denote the size of the largest gap between consecutive primes below X. Answering ...
AbstractLetG(X) denote the largest gap between consecutive primes belowX. Improving earlier results ...
We show that there exist pairs of consecutive primes less than x whose difference is larger than t(1...
Let pn denote the n-th prime, and for any k > 1 and sufficiently large X , define the quantity Gk...
AbstractLet G(x;q,a):=maxPn⩽x(Pn+1−Pn),Pn‵Pn+1‵amodq where (a, q) = 1 and Pn, Pn + 1 are consecutive...
Abstract. Let n be a natural number. If the sum of the proper divisors of n is less than n, then n i...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
Let q > r ≥ 1 be coprime integers. Let P c = P c ( q , r , H ) be an ...
Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes ...
We show that the existence of arithmetic progressions with few primes, with a quantitative bound on ...
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving...
For a positive integer $n$, we denote by $F(n)$ the distance from $n$ to the nearest prime number. W...
Let pn denote the n-th prime. We prove that max/pn+1 ≤ X (pn+1 - pn) ≫ log X log log X log log log l...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...