Problem 141

Erdős Problem #141: declared status 'open'. Formalized: yes. Let $k\geq 3$. Are there $k$ consecutive primes in arithmetic progression? Current best: The existence of such progressions for small $k$ has been verified for $k\leq 10$, see the Wikipedia page. Prize: no. OEIS: A006560. Tags: additive combinatorics, arithmetic progressions, primes.