SanD Primes and Numbers
Freeman J. Dyson
Institute of Advanced Study
Princeton, NJ 08540
Norman E. Frankel
School of Physics
University of Melbourne
Anthony J. Guttmann
School of Mathematics and Statistics
The University of Melbourne
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,... .
Full version: pdf,
Received April 17 2019; revised version received July 22 2019; January 7 2020.
Published in Journal of Integer Sequences,
February 24 2020.
Journal of Integer Sequences home page