🏆

Prime Number Theorem

★★★★★Graduate+

📖Definition

The Prime Number Theorem states that π(x), the count of primes ≤ x, is asymptotic to x/ln(x).

π(x) ∼ (x)/(ln x)

lim_x → ∈fty (π(x))/(x / ln x) = 1

Precise asymptotic form

예제 1

Estimate the number of primes up to 1000.

Discovered by: Hadamard, de la Vallée Poussin (1896)

Conjectured by Gauss; proved independently by Hadamard and de la Vallée Poussin.

Large prime generation

Prime distribution

#소수#정리#prime#theorem