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Remark: ALBERT AFLITUN'S NUMBER THEORY FOURTH PROBLEM is connected with L. R. Aflitun Ptolmis's conjecture: "EVERY EVEN NUMBER CAN BE REPRESENTED AS A DIFFERENCE OF TWO CONSECUTIVE PRIMES, AND NOT BY ONE WAY" (1799), - and with De Polignac's conjecture: "EVERY EVEN NUMBER IS THE DIFFERENCE OF TWO CONSECUTIVE PRIMES IN INFINITELY MANY WAYS (1849) (all problems are unsolved).
ADDITIONALLY ONE CAN FORMULATE NEW CONJECTURES ON FUNCTIONS β(k) and δ(k).