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CS1975

F. Cohen and J. L. Selfridge, "Not every number is the sum or difference of two prime powers," Math. Comp., 29 (1975) 79--81.  Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday.  MR0376583

Abstract: Every odd number less than 262144 is the sum or difference of a power of two and a prime. An interesting example is 113921 = p-2¹⁴¹. Using covering congruences, we exhibit a 26-digit odd number which is neither the sum nor difference of a power of two and a prime. This method is modified ot exhibit an arithmetic progression of numbers which are not the sum or difference of two prime powers.