The Goldbach Conjecture and Dirichlet's Theorem

The Goldbach Conjecture says any even number greater than 2 can be written as the sum of 2 primes. 

Dirichlet's Theorem says that there are infinitely many primes of the form n*a + b, where a and b are coprime (have no factors in common) and n is any positive integer. 

Some examples:

17 + 3 = 20

2*2 + 3 = 7

2*991 + 977 = 2819 

991, 997, and 2819 are all prime, and 991 and 977 are coprime. 

Primes of arbitrary size can be made by using the conjecture and theorem together. 

Dirichlet's Theorem is the key to solving the integer factorization problem in my opinion.