Integers such that Difference with Power of 2 is always Prime/Examples/75

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

The positive integer $75$ has the property that such that:

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

is prime whenever it is (strictly) positive.

Proof

\(\ds 75 - 2^1\)

\(=\)

\(\ds 73\)

which is prime

\(\ds 75 - 2^2\)

\(=\)

\(\ds 71\)

which is prime

\(\ds 75 - 2^3\)

\(=\)

\(\ds 67\)

which is prime

\(\ds 75 - 2^4\)

\(=\)

\(\ds 59\)

which is prime

\(\ds 75 - 2^5\)

\(=\)

\(\ds 43\)

which is prime

\(\ds 75 - 2^6\)

\(=\)

\(\ds 11\)

which is prime

\(\ds 75 - 2^7\)

\(=\)

\(\ds -53\)

which is not positive

$\blacksquare$