AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime for x \2>1. We prove, building on work of Erd\”os, analogues of this result, in which the interval is of the form (x, zx) and there are at least m primes ≡ a(mod d) required to be contained in this interval, and where z, a and d have to satisfy some conditions. For the case m 1 the results are worked out using a computer. They can be found in Table 1
AbstractLet Nm(x) be the number of arithmetic progressions that consist of m terms, all primes and n...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Theorem. There are infinitely many primes. Euclid’s proof of this theorem is a classic piece of math...
AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime fo...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Let d be a squarefree integer and consider the subclass of primes with Legendre symbol ( d/p ) = +1....
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
We prove that every interval xð1 D1Þ; x contains a prime number with D 28 314 000 and provided xX...
In 1845 Bertrand postulated that there is always a prime between n and 2n, and he verified this for ...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
Almost all short intervals containing prime numbers by Chaohua Jia (Beijing) 1. Introduction. In 193...
Abstract In this note, we prove that for n ≥ 30, there exists at lest a prime number in the interval...
This work presents a study of prime numbers, how they are distributed, how many prime numbers are t...
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provid...
We discuss the formalization, in the Matita Interactive Theorem Prover, of some results by Chebyshev...
AbstractLet Nm(x) be the number of arithmetic progressions that consist of m terms, all primes and n...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Theorem. There are infinitely many primes. Euclid’s proof of this theorem is a classic piece of math...
AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime fo...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Let d be a squarefree integer and consider the subclass of primes with Legendre symbol ( d/p ) = +1....
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
We prove that every interval xð1 D1Þ; x contains a prime number with D 28 314 000 and provided xX...
In 1845 Bertrand postulated that there is always a prime between n and 2n, and he verified this for ...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
Almost all short intervals containing prime numbers by Chaohua Jia (Beijing) 1. Introduction. In 193...
Abstract In this note, we prove that for n ≥ 30, there exists at lest a prime number in the interval...
This work presents a study of prime numbers, how they are distributed, how many prime numbers are t...
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provid...
We discuss the formalization, in the Matita Interactive Theorem Prover, of some results by Chebyshev...
AbstractLet Nm(x) be the number of arithmetic progressions that consist of m terms, all primes and n...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Theorem. There are infinitely many primes. Euclid’s proof of this theorem is a classic piece of math...
DOI
Add to ORKG