Prime Number Calculator

Check if numbers are prime, find prime factors, generate prime lists, and explore the fascinating world of prime numbers

✓ Prime checking ✓ Prime factorization ✓ Prime generation

Prime Number Tools

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 Properties

• 2 is the only even prime number
• All primes > 2 are odd
• There are infinitely many primes
• Every integer > 1 has a unique prime factorization
• Twin primes differ by 2 (e.g., 11 and 13)

Famous Prime Numbers

Largest known prime 2^82,589,933 - 1
Mersenne prime 2^p - 1
Fermat prime 2^(2^n) + 1
Sophie Germain p, 2p+1 both prime
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Understanding Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Definition

A prime p has exactly two divisors: 1 and p

Fundamental Theorem

Every integer greater than 1 can be expressed uniquely as a product of prime numbers (up to the order of factors).

Applications

Cryptography

RSA encryption relies on the difficulty of factoring large composite numbers into their prime factors.

Computer Science

Hash functions, random number generation, and algorithm design often use prime numbers.

Number Theory

Prime numbers are fundamental building blocks in mathematical research and proofs.

Nature

Cicadas emerge in prime-numbered cycles (13 or 17 years) to avoid predator synchronization.