Link : https://beggarsmind.github.io/prime_number/

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has exactly two distinct positive divisors: 1 and itself.

Importance of Prime Numbers :-

*Foundation of Number Theory: Prime numbers are considered the "building blocks" of the integers because any integer greater than 1 can be expressed as a product of primes (this is known as the Fundamental Theorem of Arithmetic).

*Applications in Cryptography: Prime numbers play a crucial role in modern cryptography, especially in algorithms like RSA, which relies on the difficulty of factoring the product of two large primes.

*Mathematical Research: Primes are a subject of extensive research in mathematics, leading to many interesting theorems and conjectures, such as the Goldbach Conjecture and the Twin Prime Conjecture.

Prime Number Theorems :-

Prime Number Theorem: This theorem describes the asymptotic distribution of prime numbers. It states that the number of primes less than a given number 𝑛 n is approximately 𝑛 / log ⁡ ( 𝑛 ) n/log(n).

• Wilson's Theorem: A prime number 𝑝 p satisfies Wilson's theorem if ( 𝑝 − 1 ) ! ≡ − 1   ( mod  𝑝 ) (p−1)!≡−1 (mod p). This means that the factorial of 𝑝 − 1 p−1, when divided by 𝑝 p, leaves a remainder of -1.