Not every number is the sum or difference of two prime powers

Authors:
Fred Cohen and J. L. Selfridge

Journal:
Math. Comp. **29** (1975), 79-81

MSC:
Primary 10J15; Secondary 10-04

DOI:
https://doi.org/10.1090/S0025-5718-1975-0376583-0

MathSciNet review:
0376583

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Abstract: Every odd number less than 262144 is the sum or difference of a power of two and a prime. An interesting example is . 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. The method is then modified to exhibit an arithmetic progression of numbers which are not the sum or difference of two prime powers.

**[1]**P. Erdös,*On integers of the form 2^{𝑘}+𝑝 and some related problems*, Summa Brasil. Math.**2**(1950), 113–123. MR**0044558**

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DOI:
https://doi.org/10.1090/S0025-5718-1975-0376583-0

Article copyright:
© Copyright 1975
American Mathematical Society