 # Prime Numbers

Prime numbers are the numbers with two factors, 1 and the number itself. It can be divided evenly by the two factors. For example, 7 is a prime number, which is divisible by 1 and 7 only. If we divide 7 with any other number then a fraction value is produced. The contradictory part of a prime number is a composite number, which has more than two factors. In the number system, we have learned many types of numbers out of which prime and composite numbers are the most significant ones.

## 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.

## List of Prime Numbers 1 to 100

As we know, the prime numbers are the numbers which have only two factors which are 1 and the numeral itself. There are a number of primes in the number system. Let us provide here the list of prime numbers that are present in 1 to 100 numbers along with their factors and prime factorisation.

 Prime Numbers from 1 to 100 Factors Prime Factorisation 2 1, 2 1 x 2 3 1, 3 1 x 3 5 1,5 1 x 5 7 1,7 1 x 7 11 1,11 1 x 11 13 1, 13 1 x 13 17 1, 17 1 x 17 19 1, 19 1 x 19 23 1, 23 1 x 23 29 1, 29 1 x 29 31 1, 31 1 x 31 37 1, 37 1 x 37 41 1, 41 1 x 37 43 1, 43 1 x 43 47 1, 47 1 x 47 53 1, 53 1 x 53 59 1, 59 1 x 59 61 1, 61 1 x 61 67 1, 67 1 x 67 71 1, 71 1 x 71 73 1, 73 1 x 73 79 1, 79 1 x 79 83 1, 83 1 x 83 89 1, 89 1 x 89 97 1, 97 1 x 97

## Prime Numbers Chart

The chart below shows the list of prime numbers, which are represented in the coloured box. ### Is 1 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 a prime number. But, number 1 has one and only one factor which is 1 itself. Thus, 1 is not considered a Prime number.

Examples: 2,3,5,7,11 etc

In all the positive integers given above, all are either divisible by 1 or itself i.e exactly two positive integers.

### 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. Know how to find prime numbers online from 1 to 100.

### Example Questions:

 Example 1: Is 10 a Prime Number? Answer – No, because it can be divided evenly by 2 or 5, 2×5=10, as well as by 1 and 10. Example 2: Is 19 a Prime Number? Answer – First we need to find the number k, such that k2>19. 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, suppose, P > 1 is termed 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 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.

## Difference Between Prime Numbers and Composite Numbers

 Prime Numbers Composite Numbers A prime number has two factors only. A composite number has more than two factors It can be divided by 1 and the number itself. For example, 2 is divisible by 1 and 2 It can be divided by all its factors. For example, 6 is divisible by 2,3 and 6. Examples: 2,3,7,11,109, 113,181, 191,etc. Examples: 4,8,10,15,85,114,184, etc.

### Practice Questions

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

### 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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