Distinct primes · actual exponents · complete coverage · Constructive arithmetic

Finite prime-valuation support

n>0 ⇒ a complete distinct prime support with actual exponents and product n

Construct the shared finite data used by totient products and perfect-power profiles.

Open the definition-aware map Read the final theorem See campaign milestone T09

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Exact certificate

Fully expanded arithmetic

Inspect all 1122 native tactic lines and 81 actual proof prerequisites with every definition fully expanded.

Open the exact edition →

Focused route

Final dependency cone

Start at theorem PV0014 and follow only the lemmas and conservative definitions supporting prime_valuation_support_exists.

Trace prerequisites →
Zoom between mathematical scales: complete research atlas → research domain → proof family → T09 milestone → theorem and definition dependencies.
Major independently established statements: PV0014 prime_valuation_support_exists.
Independently verified Alpha v34 checked-use theorem family: 20 dependency-curried kernel-checked theorem bodies · 81 proof prerequisites · 19 linked definitions · 31 definition-dependency arrows · 1122 exact tactic lines · first admitted v29 · not Stable. The unchanged intuitionistic kernel and separately compiled Lean verifier independently accept all 566 bundle nodes; SHA-256 4fcb3cd45e83448776abb9e33692496a7acfa98a051cae15761826a0b15fda44.
Exact mathematical boundary: This is a shared constructive tool, not an additional major blueprint goal. The list covers every prime divisor, has no repeated primes, and contains actual prime-power values. One uses the empty support; zero is excluded.