Erdős Problem #251

Partial progress by GPT-5.4 Pro (15 Apr 2026): solution to variant problem.

Problem
Erdős problem #251 (number theory, irrationality); current status: open
Credit
GPT-5.4 Pro · AI on its own
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-04-15 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PARTIALPer Tao's AI-contributions wiki

The problem

Is

∑pn2n\sum \frac{p_n}{2^n}

irrational? (Here pnp_n is the nnth prime.)

Statement quoted from erdosproblems.com/251, maintained by Thomas Bloom. Original source: [Er58b][ErGr80,p.62][Er88c,p.103]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Outcome
15 Apr, 2026 AI on its own GPT-5.4 Pro 🟡 Solution to variant problem

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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