# Integers such that Difference with Power of 2 is always Prime/Examples/7

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

The positive integer $7$ has the property that such that:

$\forall k > 0: 7 - 2^k$

is prime whenever it is (strictly) positive.

## Proof

 $\ds 7 - 2^1$ $=$ $\ds 5$ which is prime $\ds 4 - 2^2$ $=$ $\ds 3$ which is prime $\ds 7 - 2^3$ $=$ $\ds -1$ which is not positive

$\blacksquare$