A056636 Conjecturally largest even integer which is the sum of two primes in at most n ways.

2, 12, 68, 128, 152, 188, 332, 398, 398, 488, 632, 692, 692, 992, 992, 992, 1112, 1112, 1412, 1412, 1448, 1718, 1718, 1718, 1718, 2048, 2252, 2252, 2672, 2672, 2672, 2936, 2936, 2936, 2978, 3092, 3092, 3218, 3272, 3296, 3632, 3632, 3754, 4022, 4058, 4412