DOIAbstract
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provided x⩾10726905041. The proof combines analytical, sieve and algorithmical methods
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provided x⩾10726905041. The proof combines analytical, sieve and algorithmical methods
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Abstract. We are interested in classifying those sets of primes P such that when we sieve out the in...
Suppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}N½⁺¹⁰ᵋ, ε > 0...
International audienceWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28 31...
Almost all short intervals containing prime numbers by Chaohua Jia (Beijing) 1. Introduction. In 193...
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
Abstract In this note, we prove that for n ≥ 30, there exists at lest a prime number in the interval...
We give a new estimate for the integral moments of primes in short intervals of the type (p, p + h],...
Let n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller tha...
Goldston, Pintz and Yıldırım have shown that if the primes have ‘level of distribution’ θ for some θ...
Let Ek be the set of positive integers having exactly k prime factors. We show that almost all inter...
Assuming the Riemann Hypothesis we prove that the interval [N, N + H] contains an integer which is a...
Zhang has shown there are infinitely many intervals of bounded length containing two primes. We show...
AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime fo...
Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes ...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Abstract. We are interested in classifying those sets of primes P such that when we sieve out the in...
Suppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}N½⁺¹⁰ᵋ, ε > 0...
International audienceWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28 31...
Almost all short intervals containing prime numbers by Chaohua Jia (Beijing) 1. Introduction. In 193...
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
Abstract In this note, we prove that for n ≥ 30, there exists at lest a prime number in the interval...
We give a new estimate for the integral moments of primes in short intervals of the type (p, p + h],...
Let n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller tha...
Goldston, Pintz and Yıldırım have shown that if the primes have ‘level of distribution’ θ for some θ...
Let Ek be the set of positive integers having exactly k prime factors. We show that almost all inter...
Assuming the Riemann Hypothesis we prove that the interval [N, N + H] contains an integer which is a...
Zhang has shown there are infinitely many intervals of bounded length containing two primes. We show...
AbstractBertrand's Postulate is the theorem that the interval (x, 2x) contains at least one prime fo...
Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes ...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Abstract. We are interested in classifying those sets of primes P such that when we sieve out the in...
Suppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}N½⁺¹⁰ᵋ, ε > 0...
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