Complexity classification of Weak-Bertrand within TFNP

Determine the precise complexity classification within TFNP of the search problem Weak-Bertrand: given unary input 1^n, output a prime p satisfying 2^n < p < 2^{32n}.

Background

The paper introduces oracle hierarchies within TFNP and proves self-lowness results for several subclasses, including PPA. Leveraging that factoring is (under GRH) in PPA and that PPA is self-low, the authors present results relating Weak-Bertrand to LOSSY and PPADS with PPA or PPP oracles. These results suggest new approaches to classifying the deterministic prime-generation problem within TFNP.

In this context, the authors explicitly point to a longstanding open problem regarding the precise placement of Weak-Bertrand in TFNP and present their theorems as potential steps toward resolving it.