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Is it true that :

For any positive integer $n$ such that $n \equiv 0 \pmod 6$ there is at least one prime number of the form:

$p=2^{n+a}+2^{n} + 1$ , or , $p=2^{n+a}+2^{n} - 1$

with following properties : $0 \leq a < n$ , and $a\in \mathbf{Z^{*}} ; n\in \mathbf{Z^{+}} $

I have checked statement for each $n$ up to $n=1002$ and I haven't found any counterexample.

Any idea how to prove or disprove statement above without using a computer?

  • 0
    IOW, OTF $64^m(2^a+1)\pm1,m\in\mathbb{N},0\le a<6m$.2011-11-07
  • 0
    [related sequence](http://oeis.org/A126717)2011-11-08

1 Answers 1

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The conjecture appears to be false for $n=2184$.