Add to ORKGLet n ∈ Z+. Is it true that every sequence of n consecutive integers greater than n2 and smaller than (n + 1)2 contains at least one prime number? In this paper we show that this is actually the case for every n ≤ 1, 193, 806, 023. In addition, we prove that a positive answer to the previous question for all
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provid...
Let [ ] denote the integer part. Among other results in [3] we gave a complete solution to the follo...
Legendre’s conjecture states that there is a prime number between n2 and (n + 1)2 for every positive...
It is well-known that there are infinitely many prime numbers. The ‘Twin Prime Conjecture’ states t...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Six conjectures on pairs of consecutive primes are listed below together with examples in each case....
Abstract. A new conjecture on prime numbers is proposed in this short note. Conjecture 1. Let pn den...
Dirichlet in 1837 proved that for any a, q with (a, q) = 1 there are infinitely many primes p with ...
Abstract. For positive integers n and k, it is possible to choose primes P1, P2, · · · , Pk such ...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
In 1912, Edmund Landau listed four basic problems about prime numbers in the International Congress ...
In this paper, sequence of prime numbers would be investigated in even numbers. And Goldbach’s conje...
We introduce a method for showing that there exist prime numbers which are very close together. The ...
In this paper I make the following conjecture: for any arithmetic progression a + b*k, where at leas...
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provid...
Let [ ] denote the integer part. Among other results in [3] we gave a complete solution to the follo...
Legendre’s conjecture states that there is a prime number between n2 and (n + 1)2 for every positive...
It is well-known that there are infinitely many prime numbers. The ‘Twin Prime Conjecture’ states t...
We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive inte...
Six conjectures on pairs of consecutive primes are listed below together with examples in each case....
Abstract. A new conjecture on prime numbers is proposed in this short note. Conjecture 1. Let pn den...
Dirichlet in 1837 proved that for any a, q with (a, q) = 1 there are infinitely many primes p with ...
Abstract. For positive integers n and k, it is possible to choose primes P1, P2, · · · , Pk such ...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Dirichlet’s theorem on primes in arithmetic progressions states that for any positive integer q and ...
In 1912, Edmund Landau listed four basic problems about prime numbers in the International Congress ...
In this paper, sequence of prime numbers would be investigated in even numbers. And Goldbach’s conje...
We introduce a method for showing that there exist prime numbers which are very close together. The ...
In this paper I make the following conjecture: for any arithmetic progression a + b*k, where at leas...
AbstractWe prove that every interval ]x(1−Δ−1),x] contains a prime number with Δ=28314000 and provid...
Let [ ] denote the integer part. Among other results in [3] we gave a complete solution to the follo...
Legendre’s conjecture states that there is a prime number between n2 and (n + 1)2 for every positive...