A Twin Prime Analog of Goldbach’s Conjecture
A. Dinculescu *
Formerly with “Esperion” at Western Michigan University, Kalamazoo, MI, 49008, USA.
*Author to whom correspondence should be addressed.
Abstract
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 greater than 2 can be expressed as the sum of two primes, it is conjectured that any even integer strictly larger than a prime P is the sum of two twin ranks or, equivalently, any prime number is the sum of two twin ranks minus 1. This conjecture was verified up to the 10000th prime, and no counterexample was found.
Keywords: Goldbach’s conjecture, distribution of primes, twin primes.