Add to ORKGWe show that the existence of arithmetic progressions with few primes, with a quantitative bound on "few", implies the existence of larger gaps between primes less than x than is currently known unconditionally. In particular, we derive this conclusion if there are certain types of exceptional zeros of Dirichlet L-functions.Comment: re-organized the description of the corollaries; typos correcte
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving...
Erd\H{o}s considered the second moment of the gap-counting function of prime divisors in 1946 and pr...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
peer reviewedDirichlet’s theorem on primes in arithmetic progressions states that for any positive i...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
We study the set D of positive integers d for which the equation $\phi(a)-\phi(b)=d$ has infinitely ...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...
Under the assumption of infinitely many Siegel zeroes $s$ with $Re(s)>1-\frac{1}{(\log q)^{r^r}}$ fo...
ABSTRACT. Let G(X) denote the size of the largest gap between consecutive primes below X. Answering ...
Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved...
We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to sm...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving...
Erd\H{o}s considered the second moment of the gap-counting function of prime divisors in 1946 and pr...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
peer reviewedDirichlet’s theorem on primes in arithmetic progressions states that for any positive i...
In the present work we prove a common generalization of Maynard- Tao’s recent result about consecuti...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
We study the set D of positive integers d for which the equation $\phi(a)-\phi(b)=d$ has infinitely ...
We prove a couple of related theorems including Legendre’s and Andrica’s conjecture. Key to the proo...
Under the assumption of infinitely many Siegel zeroes $s$ with $Re(s)>1-\frac{1}{(\log q)^{r^r}}$ fo...
ABSTRACT. Let G(X) denote the size of the largest gap between consecutive primes below X. Answering ...
Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved...
We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to sm...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimat...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...