The even integers from 4 to 28 as sums of two primes: Even integers correspond to horizontal lines. For each prime, there are two oblique lines, one red and one blue. The sums of two primes are the intersections of one red and one blue line, marked by a circle. Thus the circles on a given horizontal line give all partitions of the corresponding even integer into the sum of two primes.
“Goldbach’s conjecture, I finally remember it,” he says, as I’m standing to go. “And I want to make sure I tell you. It’s important: For every even number n>2, there exist two prime numbers p_1 and p_2 such that we can write: p_1 + p_2 = n…”
Goldbach's conjecture on Wikipedia.Wikipedia 