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The prime divisors of integers: the theorem that every integer greater than 1 has a prime divisor, smallest prime factors, the set of primes dividing a given integer, and related elementary divisibility facts. Unique factorization itself, and prime-distribution questions such as gaps or counting functions, belong under their own tags.

Every integer greater than 1 has a prime divisor.

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 0.10, 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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