Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 7

Problem 200

Statement. Does the longest arithmetic progression of primes in $\{1,\ldots,N\}$ have length $o(\log N)$ ?

Status. Open.

Source. erdosproblems.com/200, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #200, https://www.erdosproblems.com/200.

Formalization. Statement in formal-conjectures.

Progress

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Known Results

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Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

Linked from (6)

Sumsets and Arithmetic Progressions additive_combinatorics/erdos_1979_old_new_problems_results_combinatorial_number additive_combinatorics/grosswald_1982_arithmetic_progressions_that_consist_only_primes Corollary (p. 12): if the conditional formula (2) holds, the primes contain arbitrarily long arithmetic progressions Theorem 1 (p. 11): a strong form of the Hardy–Littlewood Theorem X_1 would give the asymptotic count of m-term prime progressions up to x Theorem 2 (p. 12): an unconditional asymptotic series for the number of three-term prime progressions up to x

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