Two reversed primes in prime bases

From papers

Let bb be a fixed prime, and let p\overleftarrow{p} denote the digit reversal of a prime pp in base bb. Two-reversed-prime conjecture. Every sufficiently large even integer NN can be expressed as

N=p1+p2.N=\overleftarrow{p_1}+\overleftarrow{p_2}.

The analogous assertion fails infinitely often for infinitely many composite bases, including base 1010, 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.

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Sources & referencesView supporting material

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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