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The theorem (Euclid's) that there are infinitely many prime numbers, and related claims: classical and alternative proofs (Euler's analytic proof, Furstenberg's topological proof), quantitative strengthenings, infinitude statements for primes of special forms where no specific conjecture tag applies, and analogues in other rings or settings. Statements about specific hard prime-distribution proble

There are infinitely many prime numbers.

VerifiedThe evidence, examined directly, establishes the claim.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 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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