Dubner's conjecture


Dubner's conjecture is an as yet unsolved conjecture by American mathematician Harvey Dubner. It states that every even number greater than 4208 is the sum of two t-primes, where a t-prime is a prime which has a twin. The conjecture is computer-verified for numbers up to
Even numbers that make an exception are: 2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518, 784, 786, 788, 904, 906, 908, 1114, 1116, 1118, 1144, 1146, 1148, 1264, 1266, 1268, 1354, 1356, 1358, 3244, 3246, 3248, 4204, 4206, 4208.
The conjecture, if proved, will prove both the Goldbach's conjecture and the twin prime conjecture.
Whilst already itself a generalization of both these conjectures, the original conjecture of Dubner may be generalized even further: