Prime Number Checker

🔢 Primes from 1 to 100

Highlighted in purple — all 25 prime numbers under 100

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

There are 25 prime numbers between 1 and 100. The next primes continue: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97...

🚀 How to Use

Three modes available in the Prime Checker

1

Mode A: Check a Single Number

Enter any number and click Check. The tool instantly tells you if it is prime or not, and shows the full prime factorization if it is composite.

2

Mode B: Find Primes in a Range

Enter a start and end number (e.g. 100 to 200) and get a complete list of all prime numbers in that range.

3

Mode C: Prime Factorization

Enter any composite number and get its full prime factorization — the number broken down into its prime factors (e.g. 360 = 2³ × 3² × 5).

4

Copy or Download Results

Copy a single result or download a full list of primes in a range as a text file for study or reference.

📊 Interesting Prime Facts

Fact	Detail
Smallest prime	2 (also the only even prime number)
Primes under 10	2, 3, 5, 7 (four primes)
Primes under 100	25 prime numbers
Twin primes	Pairs that differ by 2: (3,5), (11,13), (17,19), (41,43)...
Mersenne primes	Primes of the form 2ⁿ-1: 3, 7, 31, 127, 8191...
Largest known prime	As of 2024: 2^136,279,841-1 (over 41 million digits)
Are there infinite primes?	Yes — proven by Euclid around 300 BC

✨ Pro Tips

⚡

Quick Divisibility Check

Before using the tool, try quick checks: if a number ends in 0,2,4,5,6,8 it's NOT prime (divisible by 2 or 5). If its digits sum to a multiple of 3, it's divisible by 3.

🔐

Primes in Cryptography

RSA encryption — used to secure the internet — relies on the difficulty of factoring very large numbers into their prime factors. The security of HTTPS depends on primes.

🌀

Sieve of Eratosthenes

The ancient method to find all primes up to N: list numbers, start at 2, and cross out all multiples. Numbers left uncrossed are prime. Still one of the fastest methods today.

📐

Prime Factorization Use

Prime factorization is used to find the GCD (Greatest Common Divisor) and LCM (Lowest Common Multiple) of two numbers — essential in simplifying fractions and solving math problems.

❓ Frequently Asked Questions

What is a prime number? +

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, it can only be divided evenly by 1 and the number itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23...

Is 1 a prime number? +

No. 1 is not considered a prime number by mathematical convention. A prime must have exactly two distinct factors (1 and itself). The number 1 only has one factor (itself), so it doesn't qualify. This exclusion is important for the Fundamental Theorem of Arithmetic to work correctly.

Is 2 the only even prime? +

Yes. 2 is the only even prime number. Every other even number is divisible by 2 in addition to 1 and itself, so it has more than two factors and therefore can't be prime. This makes 2 uniquely special among all prime numbers.

What is prime factorization? +

Prime factorization is the process of breaking down a composite number into a product of prime numbers. For example: 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5. Every whole number greater than 1 has a unique prime factorization — this is called the Fundamental Theorem of Arithmetic.

How are prime numbers used in real life? +

Prime numbers are the foundation of modern cryptography. RSA encryption (used in HTTPS, banking, and email security) relies on multiplying two very large prime numbers together — the resulting product is easy to compute but extremely hard to factor back into its primes, creating a mathematical trap door for secure communication.

How large a number can the checker handle? +

The tool can check numbers up to many billions quickly using efficient primality algorithms. For extremely large numbers (millions of digits), specialized algorithms like Miller-Rabin probabilistic primality testing are used, which the tool implements for large inputs.

🔗 Related Tools

ToolHorizon