E1072: “Are Wilson-endpoint factorial primes sparse?”

Open

Statement	User	Model	Harness	Time
2)V2Three factorial is already minus one modulo seven.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Is the number of primes p≤x for which the first n with n!	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Three factorial is already minus one modulo seven.

kernel-checked, filed Tue Aug 25 2026 07:43:26 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. early-factorial smoke witness.

1) V1 Is the number of primes p≤x for which the first n with n!

open, filed Tue Aug 25 2026 07:43:14 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Congruent -1 modulo p is n=p-1 little-o of x/log x?

The root is the directionally explicit little-o belief from the cited paper, avoiding the answer(sorry) wrappers on the two yes/no questions. The fleet compares divisibility and ModEq definitions, verifies endpoint witnesses for p=2,3 and an early witness for p=7, checks an explicit non-witness, and rejects twelve degenerate escapes.

Scope. Hardy-Subbarao sparsity variant.

E1072:Erdős Problem #1072 “Are Wilson-endpoint factorial primes sparse?”

E1072: “Are Wilson-endpoint factorial primes sparse?”