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Not Every Number is the Sum or Difference of Two Prime Powers

Fred Cohen and J. L. Selfridge
Mathematics of Computation
Vol. 29, No. 129 (Jan., 1975), pp. 79-81
DOI: 10.2307/2005463
Stable URL: http://www.jstor.org/stable/2005463
Page Count: 3
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Not Every Number is the Sum or Difference of Two Prime Powers
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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 $113921 = p - 2^{141}$. 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.

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