Prime twins (or twin primes)
are odd prime numbers that come in pairs:
(A) Every even number n > 4208 can be written as a sum of two twin primes.
(B) Every positive even number can be written as a difference of two twin primes.
For comparison, here are two famous (weaker) conjectures:
Goldbach's conjecture: Every even number n > 2 can be written as a sum of two primes.
Twin prime conjecture: There are infinitely many twin primes.
If statements (A) and (B) are true, then Goldbach's conjecture must be true and the twin prime conjecture must be true, too.
The table below presents a partial computational check of the above statements (A) and (B).
For each n, the table shows only one of many existing representations of n as a difference of twin primes;
n # of sums -p+q p+q (n as a sum/difference of two twin primes p and q)