AbstractLetG(X) denote the largest gap between consecutive primes belowX. Improving earlier results of Erdős, Rankin, Schönhage, and Maier-Pomerance, we proveG(X)⩾(2eγ+o(1)) logXlog2Xlog4X(log3X)−2,where logνXdenotes theν-fold iterated logarithm function andγis Euler's constant. The new tool used is a combinatorial result proved by probabilistic methods
Our objective is to provide an upper bound for the length ℓN of the longest run of consecutive integ...
AbstractLet ϵ(N) > 0 be a function of positive integers N and such that ϵ(N) → 0 and Nϵ(N) → ∞ as N ...
AbstractFork>2 andr⩾2, letG(k,r) denote the smallest positive integergsuch that every increasing seq...
AbstractLetG(X) denote the largest gap between consecutive primes belowX. Improving earlier results ...
AbstractLet G(x;q,a):=maxPn⩽x(Pn+1−Pn),Pn‵Pn+1‵amodq where (a, q) = 1 and Pn, Pn + 1 are consecutive...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
Let G(X) denote the size of the largest gap between consecutive primes below X. Answering a question...
We show that there exist pairs of consecutive primes less than x whose difference is larger than t(1...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
ABSTRACT. Let G(X) denote the size of the largest gap between consecutive primes below X. Answering ...
In this paper I make the following conjecture: for any arithmetic progression a + b*k, where at leas...
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...
Let qn denote the nth number that is a product of exactly two distinct primes. We prove that qn+1 - ...
Let pn denote the n-th prime, and for any k > 1 and sufficiently large X , define the quantity Gk...
Our objective is to provide an upper bound for the length ℓN of the longest run of consecutive integ...
AbstractLet ϵ(N) > 0 be a function of positive integers N and such that ϵ(N) → 0 and Nϵ(N) → ∞ as N ...
AbstractFork>2 andr⩾2, letG(k,r) denote the smallest positive integergsuch that every increasing seq...
AbstractLetG(X) denote the largest gap between consecutive primes belowX. Improving earlier results ...
AbstractLet G(x;q,a):=maxPn⩽x(Pn+1−Pn),Pn‵Pn+1‵amodq where (a, q) = 1 and Pn, Pn + 1 are consecutive...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
Let G(X) denote the size of the largest gap between consecutive primes below X. Answering a question...
We show that there exist pairs of consecutive primes less than x whose difference is larger than t(1...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
ABSTRACT. Let G(X) denote the size of the largest gap between consecutive primes below X. Answering ...
In this paper I make the following conjecture: for any arithmetic progression a + b*k, where at leas...
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...
Let qn denote the nth number that is a product of exactly two distinct primes. We prove that qn+1 - ...
Let pn denote the n-th prime, and for any k > 1 and sufficiently large X , define the quantity Gk...
Our objective is to provide an upper bound for the length ℓN of the longest run of consecutive integ...
AbstractLet ϵ(N) > 0 be a function of positive integers N and such that ϵ(N) → 0 and Nϵ(N) → ∞ as N ...
AbstractFork>2 andr⩾2, letG(k,r) denote the smallest positive integergsuch that every increasing seq...
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