Displaying similar documents to “A remark on Chen's theorem”

On the unimodal character of the frequency function of the largest prime factor

Jean-Marie De Koninck, Jason Pierre Sweeney (2001)

Colloquium Mathematicae

Similarity:

The main objective of this paper is to analyze the unimodal character of the frequency function of the largest prime factor. To do that, let P(n) stand for the largest prime factor of n. Then define f(x,p): = #{n ≤ x | P(n) = p}. If f(x,p) is considered as a function of p, for 2 ≤ p ≤ x, the primes in the interval [2,x] belong to three intervals I₁(x) = [2,v(x)], I₂(x) = ]v(x),w(x)[ and I₃(x) = [w(x),x], with v(x) < w(x), such that f(x,p) increases for p ∈ I₁(x), reaches its maximum...

Modifications of the Eratosthenes sieve

Jerzy Browkin, Hui-Qin Cao (2014)

Colloquium Mathematicae

Similarity:

We discuss some cancellation algorithms such that the first non-cancelled number is a prime number p or a number of some specific type. We investigate which numbers in the interval (p,2p) are non-cancelled.

An Invitation to Additive Prime Number Theory

Kumchev, A., Tolev, D. (2005)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55. The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.