The number of primes is infinite. The first ones are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 and so on. The first proof of this important theorem was provided by the ancient Greek mathematician Euclid.

Infinity is not a real number, it is an idea. An idea of something without an end. Infinity cannot be measured. Even these faraway galaxies can't compete with infinity.

But there are exceptions: the 'twin primes', which are pairs of prime numbers that differ in value by just 2. Examples of known twin primes are 3 and 5, 17 and 19, and 2,003,663,613 × 2^{195,000} − 1 and 2,003,663,613 × 2^{195,000} + 1. The 'twin prime conjecture' holds that there is an infinite number of such twin pairs.

We can multiply infinity by two and have 2 ω. We can add one to it and have ω + 1. These are all hyperreal numbers. We can even square the infinity and have ω^{2}.

Different infinite sets can have different cardinalities, and some are larger than others. Beyond the infinity known as ℵ_{0} (the cardinality of the natural numbers) there is ℵ_{1} (which is larger) … ℵ_{2} (which is larger still) … and, in fact, an infinite variety of different infinities.

So here if we multiply 1 by 1 i.e 1 × 1 = 1 itself the 1 as whole number, so Yes 1 is a perfect square, whenever we multiply the number by itself we will get a perfect square.

When 0 is divided by 2, the resulting quotient turns out to also be 0—an integer, thereby classifying it as an even number. Though many are quick to denounce zero as not a number at all, some quick arithmetic clears up the confusion surrounding the number, an even number at that.

The concept of infinity in mathematics allows for different types of infinity. The smallest version of infinity is aleph 0 (or aleph zero) which is equal to the sum of all the integers. Aleph 1 is 2 to the power of aleph 0. There is no mathematical concept of the largest infinite number.

Pi is finite, whereas its expression is infinite. Pi has a finite value between 3 and 4, precisely, more than 3.1, then 3.15 and so on. Hence, pi is a real number, but since it is irrational, its decimal representation is endless, so we call it infinite.

Looking at this short list of prime numbers can already reveal a few interesting observations. First, except for the number 2, all prime numbers are odd, since an even number is divisible by 2, which makes it composite.

A prime number is a whole number greater than 1 with only two factors – themselves and 1. A prime number cannot be divided by any other positive integers without leaving a remainder, decimal or fraction. An example of a prime number is 13. Its only divisors are 1 and 13.