Integers such that Difference with Power of 2 is always Prime/Examples/15

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Example of Integers such that Difference with Power of 2 is always Prime

The positive integer $15$ has the property that such that:

$\forall k > 0: 15 - 2^k$

is prime whenever it is (strictly) positive.


Proof

\(\ds 15 - 2^1\) \(=\) \(\ds 13\) which is prime
\(\ds 15 - 2^2\) \(=\) \(\ds 11\) which is prime
\(\ds 15 - 2^3\) \(=\) \(\ds 7\) which is prime
\(\ds 15 - 2^4\) \(=\) \(\ds -1\) which is not positive

$\blacksquare$