No pairs were "discarded." Persons considering a solution to this Conjecture are chiefly interested in general cases, not special cases where prime1 equals prime2. The investigations listed above and below your comment explore cases where the even number's prime flanks are equidistant from the even number's half. For example, for 14, the primes are 3 & 11 (each is the same distance from 7). For 38, the primes are 7 & 31 (each equidistant from 19); and for 122, the primes are 43 & 79 (each equidistant from 61)...though there are other Goldbach pairs. This problem is so fascinating, I can't see why some mathematicians say its solution is trivial or irrelevant. On one site, someone wrote that pursuing it was a total waste of time! END

No pairs were "discarded." Persons considering a solution to this Conjecture are chiefly interested in general cases, not special cases where prime1 equals prime2. The investigations listed above and below your comment explore cases where the even number's prime flanks are equidistant from the even number's half. For example, for 14, the primes are 3 & 11 (each is the same distance from 7). For 38, the primes are 7 & 31 (each equidistant from 19); and for 122, the primes are 43 & 79 (each equidistant from 61)...though there are other Goldbach pairs. This problem is so fascinating, I can't see why some mathematicians say its solution is trivial or irrelevant. On one site, someone wrote that pursuing it was a total waste of time! END