Prime Number Calculator

Check if a number is prime, generate prime numbers, find factors, and explore prime number properties

Prime Number Tools

Prime Number Checker

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Prime Number Generator

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Click "Generate Primes" to see prime numbers in the range

Factor Finder

Find all factors of a number

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Find nearest primes

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Prime Number Information

Use the tools on the left to explore prime numbers and see detailed analysis here.

First 25 Prime Numbers

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

Prime Number Facts

• 2 is the only even prime number

• There are infinite prime numbers

• Prime gaps can be arbitrarily large

• Every integer > 1 has a unique prime factorization

Understanding Prime Numbers

What are Prime Numbers?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11...

Prime vs Composite

Numbers greater than 1 are either prime or composite. Composite numbers can be factored into smaller positive integers (like 6 = 2 × 3).

The Sieve of Eratosthenes

An ancient algorithm to find all primes up to a given number by iteratively marking multiples of each prime as composite.

Applications

Primes are fundamental in cryptography (RSA encryption), computer science, and pure mathematics. They're the "building blocks" of all integers.