Erdős Problem 1072

formal-conjectures · erdos-problems · ams-11

Erdős, Hardy, and Subbarao [HaSu02], believed that the number of $p \le x$ for which $f(p)=p−1$
is $o(x/\log x)$.

[HaSu02] Hardy, G. E. and Subbarao, M. V., _A modified problem of Pillai and some related questions._
Amer. Math. Monthly (2002), 554--559.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.erdosproblems.com/1072
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/1072.lean
Local target: Corpus.Erdos1072.erdos_1072.variants.littleo
Source SHA-256: 454652b1b3c7c06cb4f860f38eea0a48476e0f6b5d305132fc5a608d9b060e04
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record