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