Prime Number Theorem
- Natural & Formal Sciences -
Mathematics & Logic Dictionary
Definition
Asymptotic result in analytic number theory stating that the prime-counting function π(x), the number of primes ≤ x, satisfies π(x) ~ x / log x as x → ∞; more precisely, π(x) / (x / log x) → 1.
Prime Number Theorem
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
The asymptotic statement that π(x), the prime-counting function, satisfies π(x) ~ x / log x as x → ∞, meaning the ratio π(x) / (x / log x) tends to 1; equivalently, primes have density about 1 / log x near x.