About: Maier's theorem

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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 a 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 limit superior is greater than 1, and the limit inferior 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 a 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 limit superior is greater than 1, and the limit inferior 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)
  • Inom talteori är Maiers sats, bevisad av 1985, en sats om primtal i korta intervall. Satsen säger att om π är primtalsfunktionen och λ är större än 1 saknar ett gränsvärde då x närmar sig oändlighet. (sv)
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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 a 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 limit superior is greater than 1, and the limit inferior 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)
  • Inom talteori är Maiers sats, bevisad av 1985, en sats om primtal i korta intervall. Satsen säger att om π är primtalsfunktionen och λ är större än 1 saknar ett gränsvärde då x närmar sig oändlighet. (sv)
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  • Maier's theorem (en)
  • Maiers sats (sv)
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