prime number theorem

Definitions

1. 1

   The theorem that the number of prime numbers less than n asymptotically approaches n /…

   The theorem that the number of prime numbers less than n asymptotically approaches n / ln(n) as n approaches infinity.

   • But we cannot infer from them the equivalence in any sense of these two propositions, since we have used in our proof of the prime number theorem a subsidiary theorem on the order of magnitude of #92;zeta'(s)#47;#92;zeta(s).
2. 2

   Any theorem that concerns the distribution of prime numbers.

   • In [6], [11], abstract prime number theorems are proved under a variety of conditions.

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