Problem Statement
Does the longest arithmetic progression of primes in $\{1,\ldots,N\}$ have length $o(\log N)$?
Categories:
Primes Arithmetic Progressions
Progress
It follows from the prime number theorem that such a progression has length $\leq(1+o(1))\log N$.Source: erdosproblems.com/200 | Last verified: January 14, 2026