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Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.

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Dickson's Conjecture open

Simultaneous primality for linear forms with no local obstruction — the linear case of Schinzel's Hypothesis H, covering twin primes and prime k-tuples. Every nontrivial case is open.

Posed by Leonard Eugene Dickson · 1904 · number theory · difficulty 5/5

prime-patterns

Schinzel's Hypothesis H open

Polynomials with no local obstruction take simultaneous prime values infinitely often. The master conjecture behind twin primes, Sophie Germain primes and prime k-tuples — every nonlinear case open.

Posed by Andrzej Schinzel / Wacław Sierpiński · 1958 · number theory · difficulty 5/5

prime-patterns