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Euler's theorem that the sum of reciprocals of the primes, Σ_p 1/p, diverges. Claims about the theorem's statement and proofs (Euler's, Erdős's), the refined asymptotic Σ_{p≤x} 1/p = log log x + M (Mertens), quantitative bounds and refinements, and generalizations or analogous statements for other sequences belong here; contrasting convergent sums (e.g. Brun's theorem for twin primes) belong under

The sum of the reciprocals of the prime numbers diverges.

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 · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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