Abstract
Allprimescanbeindexedbyk,asprimesmustbeintheform of 6k+1 or 6k-1. In
this paper, we explore for the set of k such that either 6k+1 or 6k-1 is
not a prime. Our method provides a uniform formula for k that can sieve
primes and twin primes as well. The uniform presents symmetry in terms
of k that works as single index in sieving. We also propose a new
conjecture that is equivalent to Twin Prime Conjecture but possibly be
easier to approach by merely exploring of sole index in term of k.