Astra Finds New Bound on Gaps Between Prime Numbers
OpenAI has introduced a new formal proof that reduces the gap constant between prime numbers to 186. This is a significant advancement in analytical number theory.
Astra Finds New Bound on Gaps Between Prime Numbers
This is one of the classic and most well-known problems in analytic number theory. The question is posed as follows: is there a constant C such that infinitely many pairs of adjacent prime numbers differ by no more than C?
The finiteness of such a gap was first proven only in 2013. In 2014, the Polymath8 project led by Terence Tao reduced the constant to 246, and just recently, Julia Stadlmann has pushed it down to 240.
Astra has lowered C to 186: OpenAI has released a formal proof in Lean. Details on GitHub
It is not stated that the model discovered the estimate entirely autonomously. Additionally, the result relies on three axioms that exist in the literature but have not been formally proven in Lean. Still, a result is a result. OpenAI also claims to have improved a term in the estimate of large gaps between primes, which has remained unchanged for over 80 years.
Why it matters
AnalysisThis discovery is significant for analytic number theory as it reduces the gap between prime numbers, potentially influencing further research in this field.
Discuss in community
Share your questions and insights with developers
Related in Ecosystem
Practical guides, core terminology, and agent skills
Codex Skills for Beginners: Automating AI Agent Workflows
A comprehensive hands-on guide to building and executing Codex Skills: SKILL.md anatomy, explicit vs. auto-triggering, skills vs. scripts vs. tools, Skills API, and safety boundaries.
GPT Mini (Compact Models of the GPT-4o Mini Series)
An economical and ultra-fast version of OpenAI's flagship models. Optimized for mass daily tasks, instant responses, text classification, and limit conservation.
OpenAI GPT (Flagship Models of the GPT Series)
The primary universal line of large language models from OpenAI (GPT-4, GPT-4o). Optimized for complex text analysis, programming, creativity, and daily intellectual tasks.
Four Resume Tips from OpenAI’s Head of Applied AI Development
Wulfie Bain, OpenAI’s head of applied AI development, shared four resume rules: keep it short, remove irrelevant details, highlight outcomes, and lead with the strongest achievements.