Similarly as in problem/question proposed by Professor Malčeski concerning two equations p – q= 2k, q – r = 2k (with primes p and q and a positive integer k), this problem consists in the search of a prime p such that p + 6k, p + 12k and p + 18k are all primes (for a fixed given positive integer k). If the previously mentioned condition „...search of a prime p...“ we replace by the condition „...search of an integer p...“, then the related problem becomes a particular case (with k = 4) of unsolved Dickson's conjecture stated by Dickson (Dickson, L. E. (1904), "A new extension of Dirichlet's theorem on prime numbers", Messenger of mathematics, vol. 33, pp. 155–161). Namely, Dickson's conjecture asserts that if for a finite set of k linear forms a_1 + b_1n, a_2 + b_2n, ..., a_k + b_kn (a_i and b_i are integers and b_i ≥ 1 for all i = 1, 2,..., k ), there does not exist any integer d dividing all the products (a_1 + b_1n )(a_2 + b_2n) ...(a_k + b_kn) for every integer n, then there exist infinitely many positive integers n for which all k numbers a_1 + b_1n, a_2 + b_2n, ..., a_k + b_kn are primes.

Nevertheless the fact that the question proposed by Professor Malčeski is in relation to the stronger particular 4-version of Dickson's conjecture, I believe that computational results and some heuristic number theory arguments would be suggested the positive answer to this question.