Prime factorization of the constants

Determine the prime factorizations of the large composite cofactors occurring in \(\consta(p)\) for \(p\gtrsim13\), and establish the general law governing the prime factorization of the integers \(\consta(p)\).

Background

The computed constants exhibit a distinctive factorization pattern: high powers of relatively small primes together with a small number of very large prime or composite factors. For several values with p≥13p\geq13, the remaining cofactors are too large to factor completely.

The paper explicitly identifies both the factorization of these individual large cofactors and the general arithmetic law behind the factorizations as unresolved questions, noting that the latter would resolve the former.

References

E.g., what are the prime factorisations of huge composite numbers ${}\sim 10{n\cdot 100}$ appearing in the decompositions of \consta(p) for p\gtrsim 13$ (see Appendix~\ref{app:data})\,? What is the law of prime factorisation for \consta(p)$, seen at work in Table~\ref{tab:valuations}\,? (The answer to the second question will solve the former.)

— New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations  (2610.08636 - Shah et al., 6 Oct 2026) in Section 6, “Open problems and perspectives,” footnote to the opening paragraph