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

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

The following positive integers are believed to be the only values of $n$ such that:

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

is prime whenever it is (strictly) positive:

$4, 7, 15, 21, 45, 75, 105$

4

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

is prime whenever it is (strictly) positive.

7

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

is prime whenever it is (strictly) positive.

15

$\forall k > 0: 15 - 2^k$

is prime whenever it is (strictly) positive.

21

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

is prime whenever it is (strictly) positive.

45

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

is prime whenever it is (strictly) positive.

75

$\forall k > 0: 75 - 2^k$

is prime whenever it is (strictly) positive.

105

$\forall k > 0: 105 - 2^k$

is prime whenever it is (strictly) positive.