---
format: "aidr-story-markdown/v1"
id: "adf3a8dd0f3eca7302ea58e78961800c5d98aa2df388bd433d03cc2977c6d874"
canonical_url: "https://aidr.today/adf3a8dd?lang=en"
title: "AI-Based Proof Finds Integer Factorization Is Subexponential"
lang: "en"
requested_lang: "en"
available_langs: ["en","vi"]
translation_fallback: null
fallback_fields: []
published_at: "2026-10-30T15:37:46.000Z"
category: "Research"
topics: ["anthropic","llm"]
source_urls: ["https://huggingnews.com/ai/update-ai-based-proof-finds-integer-factorization-is-subexponential-f0bef3f7","https://x.com/__alpoge__/status/2114930095009968506","https://x.com/AndrewCurran_/status/2114935219539345486","https://x.com/WesRoth/status/2115262276530016299","https://x.com/ElliotGlazer/status/2115977690385895828","https://x.com/scaling01/status/2114953638736957733","https://x.com/teortaxesTex/status/2114951403374584009","https://x.com/theinformation/status/2116160725030670764"]
summary: "Researchers used a new computational algorithm to show that integer factorization can be performed within a subexponential worst-case bound, building on work by Anthropic's Claude models that developed a subexponential algorithm for the 3-SAT problem to disprove the Exponential Time Hypothesis. The discovery was made on Oct. 16 using 14M output tokens without human intervention, and a similar result was reached by models from OpenAI. While the findings do not immediately compromise existing encryption standards, the breakthrough raises questions about other security assumptions used to protect internet traffic."
---

# AI\-Based Proof Finds Integer Factorization Is Subexponential

> [Open the canonical story](<https://aidr.today/adf3a8dd?lang=en>)

**Published:** 2026-10-30T15:37:46.000Z
**Category:** Research
**Topics:** anthropic, llm

## Summary

Researchers used a new computational algorithm to show that integer factorization can be performed within a subexponential worst\-case bound, building on work by Anthropic's Claude models that developed a subexponential algorithm for the 3\-SAT problem to disprove the Exponential Time Hypothesis\. The discovery was made on Oct\. 16 using 14M output tokens without human intervention, and a similar result was reached by models from OpenAI\. While the findings do not immediately compromise existing encryption standards, the breakthrough raises questions about other security assumptions used to protect internet traffic\.

## Sources

- [Story source](<https://huggingnews.com/ai/update-ai-based-proof-finds-integer-factorization-is-subexponential-f0bef3f7>)
- [Story source](<https://x.com/__alpoge__/status/2114930095009968506>)
- [Supporting source](<https://x.com/AndrewCurran_/status/2114935219539345486>)
- [Supporting source](<https://x.com/WesRoth/status/2115262276530016299>)
- [Supporting source](<https://x.com/ElliotGlazer/status/2115977690385895828>)
- [Supporting source](<https://x.com/scaling01/status/2114953638736957733>)
- [Supporting source](<https://x.com/teortaxesTex/status/2114951403374584009>)
- [Supporting source](<https://x.com/theinformation/status/2116160725030670764>)