  Dyck paths are among the most heavily studied Catalan families. This paper is
a continuation of [2]. In the paper we are dealing with the numbering of Dyck
paths, the terms of the OEIS sequence A036991 or Dyck numbers. We consider
triplets of terms of the form (t-4, t-2, t) (t is the senior term); triplets
cover 80% of A036991. Triplets include all Mersenne numbers, with each Mersenne
number being a senior term in some triplet. Triples are distributed over
A036991 ranges; both the length of the ranges and the number of triplets in the
range are counted by the terms of the OEIS sequence A001405. In addition to
triplets, there are many lone terms in the ranges, which are counted by the
terms of the OEIS sequence A116385. Each lone term (there are an infinite
number of them) is the root of an infinite ternary tree of triplets. As a
result, the sequence A036991 is a forest of such directed trees. We test the
twin prime conjecture on infinite ternary trees of A036991. We consider the
infinity theorem for pairs of prime numbers that differ by no more than 4.
