Three reversed primes in base 10

From papers

Work in base b=10b=10, and write p\overleftarrow{p} for the digit reversal of a prime pp. Base-10 ternary reversed-prime conjecture. Every sufficiently large odd integer NN can be expressed as

N=p1+p2+p3.N=\overleftarrow{p_1}+\overleftarrow{p_2}+\overleftarrow{p_3}.

The binary reversed-prime representation fails for infinitely many integers in base 1010, including the obstruction at 610n6\cdot 10^n. This conjecture is part of the proposed explanation that the reverse Schnirelmann constant in base 1010 should be 44, with even integers requiring four reversed primes.

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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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