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Deterministic factorization over prime fields

A polynomial running time in p is not polynomial in the binary input length.

Progress records 1

Understand the problem ↓

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Understanding the problem

Read the background

A polynomial running time in p is not polynomial in the binary input length. Randomized polynomial-time factorization also differs from the uniform deterministic target.

The proof invokes the companion’s uniform Hecke zero-free theorem. Its validity is a dependency of the claim; no unconditional audit of that input or result for every finite-field representation is recorded here.

Why it matters

If correct, attains the stated deterministic polynomial bit-complexity target for prime-field factorization.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The proof invokes the companion’s uniform Hecke zero-free theorem. Its validity is a dependency of the claim; no unconditional audit of that input or result for every finite-field representation is recorded here.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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