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GrgAakash/factorial-hypergraph-auxiliary-erdos

Aakash Gurung

Palomar Registrypalomar/PALOMAR-2026-08-27-000003Aug 27, 2026math.NTscore 0

A Lean 4 formalization of a quantitative solution to the auxiliary problem suggested by Erdos alongside Problem 1059. Conditional on an explicitly stated standard dimension-one upper-bound sieve theorem, the formalization proves that for every sufficiently large L there are at least ((L+1)!)^eta/(100 log L) integers n in (2L!, (L+1)!] whose prime factors all exceed L and for which n-k! is composite for every 1 <= k <= L. The formalization does not prove that n is prime and therefore does not solve the original Erdos prime problem.

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