Add to ORKGIn this note, we show that there are many infinity positive integer values of n, in which the following inequality holds [⅟₂ (((n + 1)²)/ln (n + 1) - (n²)/(ln n)) - (ln²n)/(ln ln n)] ≤ ∏ ((n + 1)²) - ∏(n²)
michaelnielsen.org/polymath1/ index.php?title=Bounded_gaps_ between_primes, Full list of author info...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
For any m ≥ 1, let Hm denote the quantity lim infn→∞(pn+m − pn). A celebrated recent result of Zhang...
In this note, we show that there are many infinity positive integer values of n, in which the follo...
In this note, we prove that for n ≥ 30, there exists at lest a prime number\ud in the interval (n²,(...
Let pi(n) denote the prime-counting function. In this paper we work with explicit formulas for pi(n)...
Let pi(n) denote the prime-counting function. In this paper we work with explicit formulas for pi(n)...
It is well-known that there are infinitely many prime numbers. The ‘Twin Prime Conjecture’ states t...
We proved that $\liminf\limits_{n \rightarrow +\infty}(p_{n+1}-p_n)=2$ where $p_n$ is the $n-th$ pri...
Abstract. For each of the functions f ∈ {ϕ, σ, ω, τ} and every natural number K, we show that there ...
Let n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller tha...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
International audienceWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28 31...
Zhang has shown there are infinitely many intervals of bounded length containing two primes. We show...
Goldston, Pintz and Yıldırım have shown that if the primes have ‘level of distribution’ θ for some θ...
michaelnielsen.org/polymath1/ index.php?title=Bounded_gaps_ between_primes, Full list of author info...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
For any m ≥ 1, let Hm denote the quantity lim infn→∞(pn+m − pn). A celebrated recent result of Zhang...
In this note, we show that there are many infinity positive integer values of n, in which the follo...
In this note, we prove that for n ≥ 30, there exists at lest a prime number\ud in the interval (n²,(...
Let pi(n) denote the prime-counting function. In this paper we work with explicit formulas for pi(n)...
Let pi(n) denote the prime-counting function. In this paper we work with explicit formulas for pi(n)...
It is well-known that there are infinitely many prime numbers. The ‘Twin Prime Conjecture’ states t...
We proved that $\liminf\limits_{n \rightarrow +\infty}(p_{n+1}-p_n)=2$ where $p_n$ is the $n-th$ pri...
Abstract. For each of the functions f ∈ {ϕ, σ, ω, τ} and every natural number K, we show that there ...
Let n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller tha...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
International audienceWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28 31...
Zhang has shown there are infinitely many intervals of bounded length containing two primes. We show...
Goldston, Pintz and Yıldırım have shown that if the primes have ‘level of distribution’ θ for some θ...
michaelnielsen.org/polymath1/ index.php?title=Bounded_gaps_ between_primes, Full list of author info...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
For any m ≥ 1, let Hm denote the quantity lim infn→∞(pn+m − pn). A celebrated recent result of Zhang...