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- 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
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.