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The Hardy–Littlewood prime k-tuples conjecture (Dickson's conjecture for linear forms): every admissible tuple of integers or linear forms — one with no local obstruction, i.e. not covering all residue classes mod any prime — takes simultaneously prime values infinitely often. Claims about the conjecture's truth, proof attempts, partial or conditional results, and its consequences (twin primes, bo

The number of twin prime pairs below x is asymptotically 2 C₂ x/(log x)².

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Number theory Twin prime conjectureimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Every admissible tuple of integers takes simultaneously prime values infinitely often.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Number theoryimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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