What is the history of the prime number theorem?

What is the history of the prime number theorem?

The prime number theorem describes the asymptotic distribution of prime numbers. Its history dates back to the 19th century.

Who were the key mathematicians involved in its development?

Key figures include Carl Friedrich Gauss, who made early conjectures, and later, Jacques Hadamard and Andrew Wiles, who proved it.

What was the significance of the theorem in mathematics?

The theorem provides a deep understanding of how primes are distributed among integers, influencing number theory and related fields.

Can you explain the theorem in simpler terms?

Sure! It essentially states that the number of primes less than a given number 'n' is approximately 'n / log(n)'.

What are some applications of the prime number theorem?

Applications include cryptography, random number generation, and algorithms in computer science.