This deposits factor route returns a partial answer that multiplies back

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.

Proposition

found.foldl (· * ·) 1 * cofactor = thousand ∧ found.length = 14 ∧ (found.filter (· == 3)).length = 4 ∧ found.all (fun p => 1 < p && cofactor % p != 0) ∧ cofactor % 2 = 1 ∧ cofactor % 3 = 1 ∧ powModBin 2 (cofactor - 1) cofactor ≠ 1 ∧ powModBin 2 4 7 = 2 ∧ powModBin 3 6 7 = 1

Proof

By decide in thousand.lean. Checked by the Lean kernel: it depends on no axiom.

Sources and identifiers

• Lean source · src/pair/lean/proofs/thousand.lean
• Typeset paper · src/research/lean-theorems.tex
• Repository deposit · doi:10.5281/zenodo.21787144
• Author · ORCID 0009-0000-7312-9778

Proved in the same file

• The thousand bit case is one hundred twenty five octaves
• The binary units tile the thousand exactly
• The thousand is the cube octave times pentagram cubed
• The thousand carries residue one mod nine
• The thousand bit case overflows the width thirty two ceiling
• The minimal register for the thousand is width thirty three
• The thousand fills between ninety seven and ninety eight percent of its register
• The thousand bit structure is decided not a quantum machine
• The sigma trapdoor is fermats difference of squares
• A wrong witness decodes nothing because a semiprime has one split
• An impossible integer with twin primes is opened blind in one reflection
• The thousand bit integer has a thousand bits and exactly four threes
• The free register is one hundred twenty two only at width four
• One address sits sixty seven bits below the one twenty eight floor under grover
• The seal exponent seven is undone by thirty one mod ninety one
• The fold mod eight misses one tamper in eight

All machine-checked theorems