Integers such that Difference with Power of 2 is always Prime/Examples/21

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

The positive integer $21$ has the property that such that:

$\forall k > 0: 21 - 2^k$

is prime whenever it is (strictly) positive.

Proof

\(\ds 21 - 2^1\)

\(=\)

\(\ds 19\)

which is prime

\(\ds 21 - 2^2\)

\(=\)

\(\ds 17\)

which is prime

\(\ds 21 - 2^3\)

\(=\)

\(\ds 13\)

which is prime

\(\ds 21 - 2^4\)

\(=\)

\(\ds 5\)

which is prime

\(\ds 21 - 2^5\)

\(=\)

\(\ds -9\)

which is not positive

$\blacksquare$