Number Theory

    

Twin Primes: a Spectral Proof of the Infinitude

Authors: Viktor Arvidsson

We prove the twin prime conjecture, asserting infinitely many integers x such that both x and x + 2 are prime. Construct an N × N diagonal matrix HN with diagonal entries Dx = 0 if x, x + 2 prime, and Dx ≥ 3 10 otherwise. The kernel dimension equals the number of twin primes up to N, denoted |TN|. A heat-trace argument on Tr[exp(−2HN)] forces |TN| → ∞, proving the theorem. We refine parameter bounds, standardize notation, and add explicit estimates for key constants.

Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Download: PDF

Submission history

[v1] 2025-06-07 20:07:13

Unique-IP document downloads: 214 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus