F. Cohen and J. L. Selfridge [CS1975] observed that the above prime number plus or minus a power of 2 can never be a prime power.
Zhi-Wei Sun [Sun2000] extended the work of Cohen and Selfridge slightly to show that none of the numbers
47867742232066880047611079 +
66483084961588510124010691590k can be written as a
sum or difference of two prime powers. [Caldwell]