prime number theorem

Noun

Meaning

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

(number theory) Any theorem that concerns the distribution of prime numbers.

Examples

D. J. Newman observed that the full strength of Ikehara's theorem is not needed for the prime number theorem, and one can get away with a special case that is much easier to prove. Source: Internet

Havil 2003, p. 171 The distribution of primes in the large, such as the question how many primes are smaller than a given, large threshold, is described by the prime number theorem, but no efficient formula for the n-th prime is known. Source: Internet

Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Source: Internet

This exclusion of certain notes leads to the statement of the prime number theorem. Source: Internet

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