Infinitely Many Primes?!
Infinitely Many Primes?! Prime numbers are one of the most fascinating aspects of Number Theory. Despite being one of the simplest to define, they have amazed mathematicians for centuries. In the post, we see, how one of the earliest theorems on prime numbers was proved by Euclid about 2000 years ago! Prime Numbers: A natural number greater than 1, that is divisible only by 1 and itself is called a prime number. In other words, if ` p \in N`, `p > 1` has only `1` and `p` as its factor, then the number `p` is called a prime number. For example `19` has no factors except `1` and itself. Thus it's a prime number. The first `20` prime numbers are listed below: ` 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29` `31, 37, 41, 43, 47, 53, 59, 61, 67, 71` Fig 1: The distribution of first 20 prime numbers (In x-axis, 10 units represent the gap between two primes) So Many Primes! It's then exciting to know certain properties of these special numbers, isn't it? Let's then see a few no...