  # List of Prime Numbers Between 1 to 100 – Know Prime, Coprime, Smallest & Largest Number

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Updated on: September 11th, 2023 Prime Numbers 1 to 100: There are different types of numbers in mathematics. Prime numbers are that category of numbers that have only two factors – 1 and the number itself. For example, 8 has factors like 2,4,8,1. On the other hand, 5 has only two factors like 1 and 5 itself. Hence, 5 is a prime number whereas 8 is a composite number. Also, note that 1 is neither a prime number nor a composite number.

Prime numbers can also be defined as the numbers that are not a product of any other two positive integers.

## What is the Prime Number?

A prime number is a number that either appears in its table or the table of 1. There is no other set of numbers that give a product of a prime number. The prime numbers have only two factors.

The first ten prime numbers are: 2,3,5,7,11,13,17,19,23,29

## List of Prime Numbers Between 1 to 100

Many prime numbers exist. The list of prime numbers from 1 to 100 are given below:

 Prime Numbers 1 and 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

### Properties of Prime Numbers

• Every number which is greater than 1 will be divided by at least 1 prime number
• To prime numbers will always be coprime to each other
• Every even positive integer greater than 2 can be written as the sum of two prime numbers.
• Other than 2, all other prime numbers are odd.

### Difference between Prime numbers and Composite numbers

 Prime Numbers Composite Numbers Has two factors only. Has more than two factors. Divided by 1 and the number itself. Divided by all its factors. Examples: 2, 3, 7, 11, 109 etc Examples: 4, 8, 10, 15, 85 etc

## What are Coprime numbers?

Two numbers that have the highest common factor (HCF) as 1 are coprime to each other.

For example:

Factors of 15= 1,3,5,15

Factors of 8= 1,2,4,8

The only common factor between 15 and 8 is 1. So, they are coprime to each other

Note that 15 and 8 are not prime numbers themselves, they are composite numbers but are coprime to each other.

## How to find the Prime Numbers?

### Method 1

To find a prime number you can use the following formula to find the prime number: 6n+1 or 6n-1. Since only 2 and 3 are the prime numbers which are consecutive in nature, other prime numbers can be found using this formula except for the multiples of prime numbers. For example:

6(1) – 1 = 5

6(1) + 1 = 7

6(2) – 1 = 11

6(2) + 1 = 13

6(3) – 1 = 17

6(3) + 1 = 19

6(4) – 1 = 23

6(4) + 1 = 25 (multiple of 5)

### Method 2

To figure out prime numbers which are greater than 40, you can use the formula:

n2 + n + 41, where n = 0, 1, 2, … 39

For example:

(0)2 + 0 + 0 = 41

(1)2 + 1 + 41 = 43

(2)2 + 2 + 41 = 47

## Smallest Prime Number

The smallest prime number is 2. For a number to be prime, it has to have only two factors i.e. 1 and the number itself. 2 is identified to be the smallest such number.

## Largest Prime Number

The Great Internet Mersenne Prime Search (GIMPS) has found that the largest prime number as of now is  2^(82,589,933) – 1 a number which has 24,862,048 digits.

## List of prime numbers from 1-1000

The list of prime numbers from 1 -1000 are given below:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.

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