Erdős Problem #971

Canonical assertion

declared status 'open'. Formalized: yes. Let $p(a,d)$ be the least prime congruent to $a\pmod{d}$ . Does there exist a constant $c>0$ such that, for all large $d$ , $p(a,d) > (1+c)\phi(d)\log d$ for $\gg \phi(d)$ many values of $a$ ? Prize: no. OEIS: A226521. Tags: number theory.

Notation is rendered from the stored source. The pinned checkout remains the exact record.

Sourcedatabase_record
Assertiontheoretical
Evidence0 spans
Standingrecorded

Provenance summary

Source: erdos_deep:971
Source type: database_record
Recorded: Jun 16, 2026, 12:00 AM
Updated: not recorded
Evidence spans: 0

Exact record identityFinding ID, frontier identity, and pinned Git source

Finding ID: vf_cf519abfaf881fbc
Frontier: vfr_0a25edabc16db143
Commit: ce8ba7d934c848408e0d91caca39e938698e3fc7
Tree: 03f7371b496485f761f91961027fd48198dc7e93

Exact source and rootsGit ce8ba7d934c8 and content-addressed ledgers

Source identity

Commit: ce8ba7d934c848408e0d91caca39e938698e3fc7
Tree: 03f7371b496485f761f91961027fd48198dc7e93
Committed: 2026-07-20T19:20:20-04:00
Repository: Open source

Content roots

Event log: sha256:a06797bc0d1b0e3c88a2f97507fe0832661e3992d8df41187a0aa6d3ceee9bde
Snapshot: sha256:1faedc24f040a60a22177b456c74b969a61ce8836082297b1835797a57b4fa56
Proposals: sha256:e69b38037814f2e8ca826942cfc50ab370993889be2913cac1c0b3e77711160f
Actor registry: sha256:665f3e1c48f0a50fac949681c0af01bdd28de2991f2cdc5cc4cddbe69df6311b
Artifacts: sha256:3d58619c5cfb7e28de2f344476e35c9f0b80709c996b2a1bfdb2e11496f7e1da