[Math] Can every even integer greater than four be written as a sum of two twin primes

Question

Thinking of Goldbach conjecture I arrived at this

$\mathrm{Conjecture}$: Every even integer greater than four can be written as a sum of two twin primes.

What do you think?

I hope this is true.
I tried to verify this up to some extent.

Answer 1

In fact, it was already a conjecture; mathworld says, "It is conjectured that every even number is a sum of a pair of twin primes except a finite number of exceptions whose first few terms are $2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518,\cdots$" ... (OEIS A007534; Wells 1986, p. 132).