Integers such that Difference with Power of 2 is always Prime/Examples/4

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

The positive integer $4$ has the property that such that:

$\forall k > 0: 4 - 2^k$

is prime whenever it is (strictly) positive.

Proof

\(\ds 4 - 2^1\)

\(=\)

\(\ds 2\)

which is prime

\(\ds 4 - 2^0\)

\(=\)

\(\ds 0\)

which is not (strictly) positive

$\blacksquare$