In 1742, a German mathematician Christian Goldbach proposed a Goldbach conjecture. The conjecture states that every even integer greater than 2 can be expressed as a sum of two prime numbers. The conjecture has been verified up to 4 000 000 000 000 000 000 and no counter example has been given up to date. Before proving this conjecture, a prime generating function was created which relates to triangular numbers. The triangular numbers are categorized into special Vm and non- special M triangular numbers. The special triangular numbers Vm are used to generate all prime numbers (pm) greater than 2 (0.375 is included among Vm to generate 2) using the function Pm=√(8Vm + 1). The Vm is obtained from Tn∩Mu2032. The proof holds true for all even integers greater than 2. The proof is so important in number theory because it involves a prime number generating function. This function may help us solve many prime number related problems. Keywords: Triangular numbers, special, non-special, Goldbach conjecture, prime numbers