Theorems
Prime Number Theorem
Also Known As PNT
Number Theory
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The prime number theorem describes how prime numbers are distributed among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.
Facts
StatementThe number of primes less than or equal to x, written pi(x), grows asymptotically like x divided by the natural logarithm of x, so their ratio approaches 1 as x grows large; equivalently, the average gap between consecutive primes near N is roughly the natural logarithm of N. 1 Cross-Tradition Connections
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