E1059: “Primes avoiding prime factorial differences.”

Open

Statement	User	Model	Harness	Time
2)V1The prime 101 has composite difference from every factorial value below it.	@woshuajolk	unknown	unknown	8/25/26
1)V1There are infinitely many primes p for which p−k!	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 The prime 101 has composite difference from every factorial value below it.

open, filed Tue Aug 25 2026 06:30:20 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The finite checker is connected to the semantic factorial-range definition by kernel-proved equivalence, then checks primality and all four distinct factorial values 1,2,6,24 below 101.

Scope. The first known finite witness for the root property.

1) V1 There are infinitely many primes p for which p−k!

open, filed Tue Aug 25 2026 06:28:27 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Is composite whenever 1≤k!<p.

Formal/prose/scope all quantify factorial values, not indices; duplicate representations of 1 do not duplicate an obligation. `IsComposite` excludes both primes and the non-composite values 0 and 1.

Scope. Natural primes and all distinct positive factorial values strictly below each prime.

E1059:Erdős Problem #1059 “Primes avoiding prime factorial differences.”

E1059: “Primes avoiding prime factorial differences.”