The integer two to the sixty-fifth plus one is composite

Proved

WorkbookSource.plus_44551

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $2^{65} + 1$ is not a prime number.

Source: InternLM Lean-Workbook, record lean_workbook_plus_44551 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_44551 : ¬ Nat.Prime (2^65 + 1)   :=  by sorry

Source