**What is a Prime Number?**

A prime number is a positive integer having exactly two factors. If p is a prime, then it’s only factors are necessarily 1 and p itself.

The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

It should be noted that 1 is a non-prime number.

**List of prime numbers from 1 to 100**

The table below shows the list of prime numbers from 1 to 100.

**Why 1 is not a prime number?**

Conferring to the definition of prime number, which states that a number should have exactly two factors, but number 1 has one and only one factor. Thus 1 is not considered as a Prime number.

**Smallest prime number**

The smallest prime number as defined by modern mathematicians is 2. To be prime, a number must be divisible only by 1 and the number itself.

**Largest prime number**

As of January 2016, the largest known prime number is **2****74,207,281**** − 1**, a number with 22,338,618 decimal digits. It was found by the Great Internet Mersenne Prime Search (GIMPS).

**How to find prime numbers:**

Let us choose any random number “A.” We can find whether this number is a prime number or not using the following method-

- Find the number k, where \(k^{2}>A\)
- If A is divisible by any prime number less than k, then A is a non-prime number,otherwise A is a Prime number.

Thus the value of k comes out to be 5, as \(5^{2}=25\). The prime numbers less than 5 are 2 and 3. Clearly, we can see that 19 is not divisible by both 2 and 3. Therefore, 19 is a prime number. |

**Note- ****An Integer P > 1 is termed as a prime number when its only divisors are 1 and P.**

**Any numeric m > 1 which is not a prime is termed as a composite.**

Each composite number can be factored into prime factors, and individually all of these are unique in nature.

**Some of the properties of primes are**:

- Every n > 1 is can be divided by some prime.
- The product is divisible by a prime ‘p’ only when ‘p’ divides one of the factors.
- A prime ‘p’ is one or the other relatively prime to a number ‘n’ or divide it.

** **

The only factors of 53 are 1 and 53. So, 53 is a prime number.
The factors of 1, 2, 4, 8,16. Hence it is a composite number and not a prime number. |