Prime Numbers

A prime number is a natural number that is divisible only 1 and itself. Euclid proved that there are infinitely many primes. Since every natural number can be written as a product of powers of primes in exactly one way, we think of the primes as the `building blocks' for the natural numbers.

Later Gauss proved his famous Prime Number Theorem which states that the number of primes A(n) not exceeding n is asymptotically equivalent to $n/\log n.$ In Figure 1 we plot the graph of this function over a large domain.

  

Figure 1: Distribution of Primes