Trying 2 as a first even number we get an answer.

To qualify for d1 or d2 I will rephrase the question:

Prove that there is only one natural number n such that n+1, n+11, n+111 are all primes.

SOLUTION:

FOR  n>2  t

The three addends are distinct  members of the set (1,2,3) therefore at least one of them is divisible by 3 and therefore cpomposite.