Deterministic generation of large primes

Develop a deterministic polynomial-time algorithm that, given unary input 1^n, outputs an n-bit prime number.

Background

The paper discusses prior work showing that solving Lossy with a factoring oracle (Lossy^{Factor}) would enable deterministic generation of large primes. The authors highlight that deterministic prime generation is a longstanding open problem.

Their new framework for TFNP-oracle hierarchies aims to shed light on such problems, and their self-lowness results for PPA provide additional context for approaching deterministic prime generation via reductions to TFNP subclasses.