Two reversed primes in prime bases
Let be a fixed prime, and let denote the digit reversal of a prime in base . Two-reversed-prime conjecture. Every sufficiently large even integer can be expressed as
The analogous assertion fails infinitely often for infinitely many composite bases, including base , because reversed primes can have large gaps caused by restrictions on their leading digits. The conjecture proposes that the binary representation should hold in every fixed prime base; the paper indicates that the ternary version is expected in most bases.
References
Primary source
Michael Harm and Daniel R. Johnston, “The reverse Goldbach problem and a refined Zsiflaw–Legeis theorem”, arXiv:2605.21876 (2026).
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