# 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 |

$\blacksquare$