Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.4

SanD Primes and Numbers


Freeman J. Dyson
Institute of Advanced Study
Princeton, NJ 08540
USA

Norman E. Frankel
School of Physics
University of Melbourne
Victoria 3010
Australia

Anthony J. Guttmann
School of Mathematics and Statistics
The University of Melbourne
Victoria 3010
Australia

Abstract:

We define SanD (Sum and Difference) numbers as ordered pairs (p, q) such that the digital sum s10(pq) = q − p = Δ > 0. We consider both the decimal and the binary cases in detail, and other bases more superficially. If both p and q are prime numbers, we refer to SanD primes. For SanD primes, we prove that, with one exception, notably the pair (2,7), the differences Δ = q−p = 14+18k, k=0,1,2,... .

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Received April 17 2019; revised version received July 22 2019; January 7 2020. Published in Journal of Integer Sequences, February 24 2020.

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