Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
IOW, OTF $64^m(2^a+1)\pm1,m\in\mathbb{N},0\le a<6m$. – anon Nov 7 '11 at 12:16
related sequence – pedja Nov 8 '11 at 6:57

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.