Historical dossier 015

Some consequences of defining mathematical objects constructively and mathematical truth effectively; A density-based approach for non-heuristic approximations of prime counting functions

A recorded P ≠ NP claim by Bhupinder Singh Anand, preserved from Woeginger’s frozen 2016 page.

Dossier: 015
Author(s): Bhupinder Singh Anand
Date recorded: 2004; 2015
Direction: P ≠ NP
Works or versions: 2
Adjudication: Not recorded
Seed source: sources/captures/woeginger-list-frozen-2016.html
Source selector: ol > li:nth-of-type(15)

Woeginger’s note — verbatim historical text

Verbatim historical text

[Not equal]: In the essay "Some consequences of defining mathematical objects constructively and mathematical truth effectively" from 2004, Bhupinder Singh Anand considers a constructive interpretation of classical first order theory in which he argues that the class P of polynomial-time languages in the P-versus-NP problem may define a mathematical concept that cannot be added as a formal mathematical symbol to the theory without inviting contradiction. In the paper "A density-based approach for non-heuristic approximations of prime counting functions" from 2015, Bhupinder Singh Anand shows that the prime divisors of any integer n are mutually independent, and concludes that any deterministic algorithm which always computes a prime factor of n is necessarily of the order O(n/log n). Hence Integer Factorising cannot be polynomial-time, whence P is not equal to NP. The paper is available at http://arxiv.org/abs/1510.04225.

Preserved from the frozen 2016 page. This is the historical layer, not the Register’s voice.

Adjudication status

Unadjudicated

Unadjudicated

No adjudication is recorded in the imported historical dossier.

Unadjudicated does not mean endorsed.

As of 24 July 2026

Links printed in the dossier

Link status checked against the held 24 July 2026 probe. A dead link does not change the claim’s status.

Link printed in the historical dossier
Live
http://arxiv.org/abs/1510.04225
200 · Link status checked 24 July 2026.

Cite this dossier

Plain text

The P versus NP Register. “Dossier 015: Some consequences of defining mathematical objects constructively and mathematical truth effectively; A density-based approach for non-heuristic approximations of prime counting functions.” As of 24 July 2026.

BibTeX

@misc{pvnp-register-015-2026,
  author = {{The P versus NP Register}},
  title = {Some consequences of defining mathematical objects constructively and mathematical truth effectively; A density-based approach for non-heuristic approximations of prime counting functions},
  year = {2026},
  note = {Dossier 015; as of 2026-07-24}
}

Event timeline

No post-seed events are recorded for this dossier. Its imported historical record remains unchanged.