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Displaying similar documents to “Generalised prime systems with periodic integer counting function”

Search for Wieferich Primes through the use of Periodic Binary Strings

Dobeš, Jan, Kureš, Miroslav (2010)

Serdica Journal of Computing

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The result of the distributed computing projectWieferich@Home is presented: the binary periodic numbers of bit pseudo-length j ≤ 3500 obtained by replication of a bit string of bit pseudo-length k ≤ 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.

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

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

Colloquium Mathematicae

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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

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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.