Add to ORKGWe show that the arithmetic mean of the firstn primes is an integer for N19/24+ numbersn ≤ N. This follows from showing that the discrepancy of the sequence consisting of the arithmetic means is N−5/24+
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
Ensino Médio::MatemáticaThis Demonstration shows the first n primes of a certain kind. In the first ...
12 páginas.In this note, we show that the set of n such that the arithmetic mean of the first n prim...
Knowledge about number theory and prime numbersEuclid proved that the number of prime numbers is inf...
Knowledge about algorithms, integers, number theory, prime numbers and SequencesDirichlet's theorem ...
A finite ncreasing sequence {pn}, (n=1, 2, 3, ・・・, t) of prime numbers, (t〓3), is called an arithmet...
We show that ∑ pn≤x pn+1−pn≥ √ pn (pn+1−pn)≪εx3/5+ε or any fixed ε>0. This improves a result of...
For any integer n ≥ 1 let P (n) and p(n) denote the greatest prime factor and smallest prime factor ...
The definition of “concatenation” in mathematics is, according to Wikipedia, “the joining of two num...
In this paper we study the sum p≤xτ(np), where τ(n) denotes the number of divisors of n, and {np} is...
A good new millenium for the primes Andrew Granville* is the Canadian Research Chair in number theor...
A new conjecture in prime number theory is established. Namely, if 0 < α < 1 then the followin...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
A prime number is that number that is only divisible by itself and by one. So far the prediction of ...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
Ensino Médio::MatemáticaThis Demonstration shows the first n primes of a certain kind. In the first ...
12 páginas.In this note, we show that the set of n such that the arithmetic mean of the first n prim...
Knowledge about number theory and prime numbersEuclid proved that the number of prime numbers is inf...
Knowledge about algorithms, integers, number theory, prime numbers and SequencesDirichlet's theorem ...
A finite ncreasing sequence {pn}, (n=1, 2, 3, ・・・, t) of prime numbers, (t〓3), is called an arithmet...
We show that ∑ pn≤x pn+1−pn≥ √ pn (pn+1−pn)≪εx3/5+ε or any fixed ε>0. This improves a result of...
For any integer n ≥ 1 let P (n) and p(n) denote the greatest prime factor and smallest prime factor ...
The definition of “concatenation” in mathematics is, according to Wikipedia, “the joining of two num...
In this paper we study the sum p≤xτ(np), where τ(n) denotes the number of divisors of n, and {np} is...
A good new millenium for the primes Andrew Granville* is the Canadian Research Chair in number theor...
A new conjecture in prime number theory is established. Namely, if 0 < α < 1 then the followin...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
A prime number is that number that is only divisible by itself and by one. So far the prediction of ...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
Ensino Médio::MatemáticaThis Demonstration shows the first n primes of a certain kind. In the first ...