In number theory, Maier's theorem () is a theorem about the numbers of primes in short intervals for which Cramér's probabilistic model of primes gives the wrong answer. The theorem states that if π is the prime counting function and λ is greater than 1 then does not have a limit as x tends to infinity; more precisely the lim sup is greater than 1, and the lim inf is less than 1. The Cramér model of primes predicts incorrectly that it has limit 1 when λ≥2 (using the Borel–Cantelli lemma).

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  • In number theory, Maier's theorem () is a theorem about the numbers of primes in short intervals for which Cramér's probabilistic model of primes gives the wrong answer. The theorem states that if π is the prime counting function and λ is greater than 1 then does not have a limit as x tends to infinity; more precisely the lim sup is greater than 1, and the lim inf is less than 1. The Cramér model of primes predicts incorrectly that it has limit 1 when λ≥2 (using the Borel–Cantelli lemma). (en)
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  • In number theory, Maier's theorem () is a theorem about the numbers of primes in short intervals for which Cramér's probabilistic model of primes gives the wrong answer. The theorem states that if π is the prime counting function and λ is greater than 1 then does not have a limit as x tends to infinity; more precisely the lim sup is greater than 1, and the lim inf is less than 1. The Cramér model of primes predicts incorrectly that it has limit 1 when λ≥2 (using the Borel–Cantelli lemma). (en)
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  • Maier's theorem (en)
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