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From: Kellen Myers on 23 Jun 2010 08:14
This fails for 2047 = 23 x 89.

The number 2048 will not appear in this table. Taking m>n, and making rows in the triangle by m, then for n=0 (the smallest entry in a row) T(m,n)=2m.

That means if 2048 is to appear, it must appear in the first 1024 rows. It does not. Checked by Mathematica:

Input:

TAB = Flatten[Table[4 m n + 2 m + 2 n + 2, {n, 1, 5000}, {m, 1, n}]];
For[k = 1, k <= 10, k++,
  p = Prime[k];
 If[
   Not[MemberQ[2^Prime[k], TAB]],
    Print[{2^Prime[k] - 1, PrimeQ[2^Prime[k] - 1]}]
   ];
  ];[/code]

Output:

  {3,True}
  {7,True}
  {31,True}
  {127,True}
  {2047,False}
 | 
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