Integers such that Difference with Power of 2 is always Prime/Examples/45

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

The positive integer $45$ has the property that such that:

$\forall k > 0: 45 - 2^k$

is prime whenever it is (strictly) positive.


Proof

\(\ds 45 - 2^1\) \(=\) \(\ds 43\) which is prime
\(\ds 45 - 2^2\) \(=\) \(\ds 41\) which is prime
\(\ds 45 - 2^3\) \(=\) \(\ds 37\) which is prime
\(\ds 45 - 2^4\) \(=\) \(\ds 29\) which is prime
\(\ds 45 - 2^5\) \(=\) \(\ds 13\) which is prime
\(\ds 45 - 2^6\) \(=\) \(\ds -19\) which is not positive

$\blacksquare$