Starting from the observation that the ratio of the number of twin primes to the number of primes up to a given number n, is similar to the ratio of the number of primes to the number of positive integers in the same interval, and from Goldbach’s conjecture that any even integer...
Open access
Research Article10.9734/BJMCS/2016/22064
Because the density of non-ranks in the interval 1...Pj is smaller than the average density of non-ranks of parent primes in the interval 1...L , where , there is an inferior limit on the number of twin ranks up to a prime Pj , and hence on the number of twin primes u...
Open access
Research Article10.9734/BJMCS/2015/16023
Fortune’s Conjecture is extended from a relatively short interval after each primorial to an infinite numbers of similar intervals on both sides of primorials, where n is a positive integer. In addition, it is shown that for every prime in the interval ,there is a number in th...
Open access
Research Article10.9734/BJMCS/2014/5701
The paper presents a framework for the construction of an elementary proof of the infinitude of twin primes. It starts from the fact that all positive integers can be divided into numbers that can lead directly to a pair of twin primes (called twin ranks) and numbers (called non-...
Open access
Research Article10.9734/BJMCS/2013/4358