Prime Number Calculator
Check Primes, Factorize & Explore Number Theory
Professional prime number calculator for primality testing, factorization, and number theory exploration. Find prime factors, generate prime lists, analyze prime gaps, and discover mathematical properties.
Trusted by mathematicians
4.9/5 rating
Fast algorithms
Prime Number Calculator
Explore prime numbers, factorization, and number theory properties
Test if a number is prime
Enter a number to check if it's prime
Understanding Prime Numbers
Discover the fascinating world of prime numbers and their properties.
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. The first primes are 2, 3, 5, 7, 11, 13...
Prime Factorization
Every integer greater than 1 can be uniquely expressed as a product of primes. This is the Fundamental Theorem of Arithmetic.
Twin Primes
Twin primes are pairs of primes that differ by 2, like (3,5), (11,13), (17,19). The Twin Prime Conjecture asks if there are infinitely many.
Prime Number Theorem
The number of primes less than n is approximately n/ln(n). Primes become less frequent but never stop appearing.
Mersenne Primes
Primes of the form 2^p - 1 where p is also prime. Examples: 3, 7, 31, 127. The largest known primes are Mersenne primes.
Cryptography
Prime numbers are essential for RSA encryption and modern cryptography. The difficulty of factoring large numbers keeps data secure.
Special Types of Prime Numbers
Mersenne Primes
- Form: 2^p - 1
- Examples: 3, 7, 31, 127
- 51 known as of 2024
- Largest known primes
Fermat Primes
- Form: 2^(2^n) + 1
- Only 5 known: 3,5,17,257,65537
- Related to polygon construction
- Rare and special
Sophie Germain Primes
- p where 2p+1 is also prime
- Examples: 2, 3, 5, 11, 23
- Important in cryptography
- Infinitely many (conjectured)
Palindromic Primes
- Read same forwards/backwards
- Examples: 2, 3, 5, 7, 11, 101
- Infinitely many (conjectured)
- Fun mathematical curiosity
Related Number Theory Tools
Explore our comprehensive suite of mathematical tools.