## 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. Any number which does not follow this is termed as composite numbers which means that they can be factored into other whole numbers.

**First Ten Prime Numbers:**

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

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

Here, all the concepts of prime numbers are covered along with various examples. The key concepts that are covered here include:

- Prime numbers 1-100
- Why 1 is Not a Prime Number?
- Smallest Prime Number
- Largest Prime Number
- How to Find Prime Numbers Easily?
- Properties of Prime Numbers

## Prime Numbers 1 to 100 List

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 the prime number which states that a number should have exactly two factors for it to be considered as a prime number. But, number 1 has one and only one factor which is 1 itself. 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 which is fulfilled by the number 2.

### Largest Prime Number

As of January 2016, the largest known prime number is 2{77,232,917} – 1, a number with 23,249,425 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 k2>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.

### Example Questions:

Example 1: Is 10 a Prime Number?
Thus the value of k comes out to be 5, as 52 = 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- **It should be noted that an integer supose, 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.

### Properties of Prime Numbers

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.

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

### Practice Questions

Question 1: Find if 53 is a prime number or not?
The only factors of 53 are 1 and 53. So, 53 is a prime number.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64. Hence it is a composite number and not a prime number. |

## Frequently Asked Questions From Prime Numbers

### How to Find Prime Numbers?

To find whether a number is prime, try dividing it with the prime numbers 2, 3, 5, 7 and 11. If the number is exactly divisible by any of these numbers, it is not a prime number, otherwise, it is a prime.

### Can Prime Numbers be Negative?

No, a prime number cannot be negative. According to its definition, a prime number is a number greater than 1 which is only divided by itself and 1.

### Which is the Largest Known Prime Number?

The number M77232917 is the largest prime number having 23,249,425 digits.

### What is the Difference Between a Prime and a Co prime Number?

A prime number is a number which is divisible by 1 and itself while a co prime number is a number which does not have any common factor between them other than 1. It should be noted that 2 prime numbers are always co-prime.

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