Prime Number Theorem

The Prime Number Theorem is a fundamental theorem in number theory that describes the asymptotic distribution of prime numbers. The theorem states that the number of primes less than or equal to a given number ( n ) is approximately ( \frac{n}{\ln(n)} ).

Key Points

• Definition: The theorem provides an asymptotic formula for the prime-counting function.
• Significance: It helps in understanding the distribution of prime numbers.
• Proof: The theorem was first proved by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896.

Applications

• Number Theory: It has profound implications in the study of prime numbers.
• Computer Science: It is used in algorithms that involve prime numbers.

More on Prime Numbers

For further reading on prime numbers, you can explore Prime Numbers.

Prime Number