Hcabdlog's conjecture

From papers

Let b2b\geq 2 be a fixed base. For a positive integer, write n\overleftarrow{n} for its digit reversal in base bb. Then p1p_1 and p2p_2 are primes, and gcd(p2,b3b)=1\gcd(\overleftarrow{p_2},b^3-b)=1. Hcabdlog's conjecture. Every sufficiently large even number NN can be expressed as

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

This conjecture suggests that the exceptional set in the corresponding prime-plus-reversed-prime representation theorem should be Ob(1)O_b(1). The parity restriction is necessary because b3bb^3-b is even, so the admissible reversed prime is odd. It is introduced as a simplified variant of a conjecture of Chourasiya and others.

Progress summary

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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).

Additional references

2 papers in this index state this conjecture (2025–2026). The statement above is taken from the most recent of them; the others are arXiv:2503.21136.

Solutions 0

No solutions have been posted yet.