Prime Number Calculator
Check if a number is prime, find primes in a range, and discover prime factorization
Prime Number Details
How to Use the Prime Number Calculator
Choose Your Mode
Select whether you want to check if a single number is prime or find all prime numbers within a specific range. Each mode provides different types of results and analysis.
Enter Your Number or Range
For single number mode, enter any positive integer. For range mode, specify the start and end numbers. The calculator can handle very large numbers and ranges up to 10,000 numbers.
Get Instant Results
The calculator immediately shows whether your number is prime, its prime factors if it's not prime, and the nearest prime numbers. For ranges, see all primes found with detailed statistics.
Explore Prime Factors
For non-prime numbers, see the complete prime factorization breakdown. This helps understand the mathematical structure of composite numbers and their building blocks.
Analyze Prime Distribution
In range mode, discover how primes are distributed across different number ranges, including the percentage of primes and gaps between consecutive primes.
Share Your Findings
Use the share feature to save your calculations or share interesting prime number discoveries with others. Perfect for educational purposes and mathematical exploration.
Prime Number Tips & Facts
2 is the only even prime number - all other even numbers are divisible by 2
Prime numbers become less frequent as numbers get larger, following the Prime Number Theorem
The largest known prime number has over 24 million digits and was discovered in 2018
Prime numbers are fundamental in cryptography and computer security algorithms
The Goldbach Conjecture suggests every even number greater than 2 is the sum of two primes
Twin primes are pairs of primes that differ by 2, like (3,5), (5,7), (11,13), and (17,19)
There are infinitely many prime numbers, as proven by Euclid around 300 BCE
Prime gaps can be arbitrarily large - there are sequences without any prime numbers
The Sieve of Eratosthenes is an ancient algorithm for finding all primes up to a given number
Mersenne primes have the form 2^p - 1 where p is also prime, and are used in prime searches