We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive integers, contains at least one prime from each coprime congruence class. We prove this conjecture first unconditionally for all 2≤q≤45000 and all t≥1 and second under ERH for almost all q≥2 and all t≥2. Furthermore, we outline heuristic arguments for the validity of the conjecture beyond the proven bounds and we compare it with related long-standing conjectures. Finally, we discuss some of its consequences
The set P(n) of all primes equal to or less than n has the obvious property that it contains exactly...
A 1955 result of J. Jakubík states that for the prime intervals p and q of a finite lattice, con(p) ...
Abstract. In this note we discuss the primes in Smarandache progressIons. For any positive integer n...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
peer reviewedDirichlet’s theorem on primes in arithmetic progressions states that for any positive i...
AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime fo...
Let n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller tha...
If $\mathcal{A}\subset\mathbb{N}$ is such that it does not contain a subset $S$ consisting of $k$ pa...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Dirichlet's theorem on arithmetic progressions says that there are infinitely many primes in any ari...
Dirichlet in 1837 proved that for any a, q with (a, q) = 1 there are infinitely many primes p with ...
Abstract. A new conjecture on prime numbers is proposed in this short note. Conjecture 1. Let pn den...
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
Almost all short intervals containing prime numbers by Chaohua Jia (Beijing) 1. Introduction. In 193...
AbstractAn interval [a,a+d] of natural numbers verifies the property of no coprimeness if and only i...
The set P(n) of all primes equal to or less than n has the obvious property that it contains exactly...
A 1955 result of J. Jakubík states that for the prime intervals p and q of a finite lattice, con(p) ...
Abstract. In this note we discuss the primes in Smarandache progressIons. For any positive integer n...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
peer reviewedDirichlet’s theorem on primes in arithmetic progressions states that for any positive i...
AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime fo...
Let n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller tha...
If $\mathcal{A}\subset\mathbb{N}$ is such that it does not contain a subset $S$ consisting of $k$ pa...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Dirichlet's theorem on arithmetic progressions says that there are infinitely many primes in any ari...
Dirichlet in 1837 proved that for any a, q with (a, q) = 1 there are infinitely many primes p with ...
Abstract. A new conjecture on prime numbers is proposed in this short note. Conjecture 1. Let pn den...
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
Almost all short intervals containing prime numbers by Chaohua Jia (Beijing) 1. Introduction. In 193...
AbstractAn interval [a,a+d] of natural numbers verifies the property of no coprimeness if and only i...
The set P(n) of all primes equal to or less than n has the obvious property that it contains exactly...
A 1955 result of J. Jakubík states that for the prime intervals p and q of a finite lattice, con(p) ...
Abstract. In this note we discuss the primes in Smarandache progressIons. For any positive integer n...
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