Proof of Dubner's Conjecture by Chern's Sieve Approach

G.C. Chern’s sieve approach[1] is implemented to prove Dubner's conjecture that all even numbers greater than 4206 are the sum of two prime numbers that have a twin. It is equivalent to finding prime 4-tuples of forms (n-m, n-m-2, n+m, n+m-2), (n-m, n-m+2, n+m, n+m-2), (n-m, n-m-2, n+m, n+m+2), and (n-m, n-m+2, n+m, n+m+2), for any 2n>4206. The calculated results, with maximum potential error exclusion, show that D(2n)>1 for 2n>2808, i.e. all even numbers greater than 2808 are the sum of two prime numbers that have a twin, and, thus, Dubner's conjecture is affirmed.