Primes not Sum of or Difference between Powers of 2 and 3

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Theorem

The sequence of prime numbers which cannot be expressed as either sum of or the difference between a power of $2$ and a power of $3$ begins:

$53, 71, 103, 107, 109, 149, 151, \ldots$

This sequence is A007644 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof



Sources