Prime gaps asymptotic classification

(*start*)
(*Mathematica*)
Clear[nn, h, n, k, m, d, dd];
nn = 20;
h = 2;(*twin primes*)N[
 Table[Sum[
   Sum[If[Mod[n, k] == 0,
      Sum[If[Mod[GCD[n/k, m], d] == 0, MoebiusMu[d]*(d), 0], {d, 1,
         GCD[n/k, m]}]*
       Sum[If[Mod[GCD[k, m + h], c] == 0, MoebiusMu[c]*(c), 0], {c, 1,
          GCD[k, m + h]}], 0], {k, 1, n}]/n, {n, 1,
    nn - h + 100}], {m, 1, nn - h}]];
N[Round[%, 10^-1]]
Table[N[If[n == 1, Log[nn - h + 100] + EulerGamma, MangoldtLambda[n]]*
    MangoldtLambda[n + h]], {n, 1, nn - h}];
N[Round[%, 10^-1]]


Clear[nn, h, n, k, m];
nn = 17;
h = 2;(*twin primes*)M4 =
 Table[Sum[
   Sum[If[Mod[n, k] == 0,
     Sum[If[Mod[GCD[n/k, m], d] == 0, MoebiusMu[d]*(d), 0], {d, 1,
        GCD[n/k, m]}]*
      Sum[If[Mod[GCD[k, m + h], c] == 0, MoebiusMu[c]*(c), 0], {c, 1,
        GCD[k, m + h]}], 0], {k, 1, n}], {m, 1, n}], {n, 1, nn - h}]

Clear[nn, h, n, k, m];
nn = 17 + 2;
h = 4;(*Cousin primes*)M4 =
 Table[Sum[
   Sum[If[Mod[n, k] == 0,
     Sum[If[Mod[GCD[n/k, m], d] == 0, MoebiusMu[d]*(d), 0], {d, 1,
        GCD[n/k, m]}]*
      Sum[If[Mod[GCD[k, m + h], c] == 0, MoebiusMu[c]*(c), 0], {c, 1,
        GCD[k, m + h]}], 0], {k, 1, n}], {m, 1, n}], {n, 1, nn - h}]
(*end*)

(*start*)
(*8 Feb 2019*)
TableForm[Table[
  h = 2^hh;
  nn = 82;
  TableForm[CC = Table[
     TableForm[
      A = Table[
        Table[If[Mod[n, k] == 0, MoebiusMu[k]/(k)^(0 - 1), 0], {k, 1,
          n}], {n, 1, nn}]];
     TableForm[
      B = Transpose[
        Table[Table[If[n >= k, A[[n, k]], 0], {k, 1, nn}], {n, 1,
          nn}]]];
     TableForm[
      AA = Table[
        Table[If[Mod[n, k] == 0, B[[n/k, m]], 0], {k, 1, nn}], {n, 1,
         nn}]];
     TableForm[
      BB = Table[
        Table[If[Mod[n, k] == 0, B[[n/k, m + h]], 0], {k, 1, nn}], {n,
          1, nn}]];
     (AA.BB)[[All, 1]], {m, 1, nn - h}]];
  Table[Sum[CC[[n, k]], {n, 1, k}], {k, 1, nn - h}], {hh, 1, 6}]]
(*end*)