Goldbach problem attempt

https://mathoverflow.net/questions/451464/a-recurrence-for-the-even-numbers-in-terms-of-a-sum-of-pairs-of-prime-numbers-i


"Mathematica start"
Clear[a, n, nn, k, t, A];
$RecursionLimit = 1000;
"Size of matrix A is nn"
nn = 42;
t[n_, k_] :=
  t[n, k] =
   If[Or[And[n == 1, k == 1], And[n == 2, k == 1]], 0,
    If[k <= 3, 1, 0]*
      If[And[PrimeQ[n] == True, PrimeQ[k] == True,
        If[And[n == 1, k == 1], 0, Mod[n + k, 2] == 0]],
       If[n >= k, (n + k), 0], 0] +
     If[k >= 4,
      If[n >= 2, 1, 0]*(t[n, k - 2] + 2)*Sign[t[n, k - 2]]*
       Product[(1 - Sign[t[n + 2*j, k - 2*j]]), {j, 1, (k - 3)}], 0]];
MatrixForm[
 A = Table[
   Table[If[
     Or[And[n == 2, k == 1], And[n == 1, k == 1],
      And[n == 2, k == 2]], 0, If[n >= k, t[n, k], 0]], {k, 1,
     nn}], {n, 1, nn}]]
DeleteCases[Flatten[A], 0]
Differences[%]
"Mathematica end"



"Mathematica start"
Clear[a, n, nn, k, t, A];
$RecursionLimit = 1000;
"Size of matrix A is nn"
nn = 400;
t[n_, k_] :=
   t[n, k] =
    If[Or[And[n == 1, k == 1], And[n == 2, k == 1]], 0,
     If[k <= 3, 1, 0]*
       If[And[PrimeQ[n] == True, PrimeQ[k] == True,
         If[And[n == 1, k == 1], 0, Mod[n + k, 2] == 0]],
        If[n >= k, (n + k), 0], 0] +
      If[k >= 4,
       If[n >= 2, 1, 0]*
        If[n >= k, (1 - Sign[Sum[t[n, j], {j, 1, k - 1}]])*(Mod[n,
            2])*(n + 3)*Sign[t[n - 2, k - 2]], 0], 0]];
MatrixForm[
  A = Table[
    Table[If[
      Or[And[n == 2, k == 1], And[n == 1, k == 1],
       And[n == 2, k == 2]], 0, If[n >= k, t[n, k], 0]], {k, 1,
      nn}], {n, 1, nn}]];
Sort[DeleteCases[Flatten[A], 0]]
Differences[%]
Differences[%]
DeleteDuplicates[%]
"Mathematica end"