A fast, local prime number checker
This prime number checker provides an instant answer to a classic mathematical question: is it prime? Whether you are working on a math assignment, exploring cryptography concepts, or simply curious about a specific large number, this tool delivers immediate results.
Because all calculations run locally in your web browser, the tool operates with zero latency. You can test massive numbers—up to 20 digits long—without waiting for a server to process the request. Your inputs remain entirely private and are never uploaded or stored.
Features of the prime number calculator
Instant Primality Testing
Type any positive integer up to 20 digits into the input field. As you type, the tool evaluates the number and immediately declares whether it is prime or composite.
Smallest Prime Factor
If your number is not prime, the calculator doesn't just stop at "no." It attempts to find the smallest prime factor, showing you exactly what the number is divisible by (e.g., "Divisible by 3"). To keep your browser responsive, this specific factor-finding step checks primes up to 1,000,000.
Neighboring Primes
Whenever you check a number, the tool automatically calculates and displays the closest prime number that comes before it, as well as the next prime number that comes after it. This is particularly useful when you are looking for prime gaps or need a prime number close to a specific magnitude.
Generate a List of Prime Numbers
Need a reference sheet? The built-in generator allows you to create a comprehensive list of prime numbers. Whether you need prime numbers up to 100 for a middle school math class, or a massive list up to 100,000 for a programming dataset, simply enter your target range and the tool will output the sequence instantly.
How the mathematical algorithms work
Handling numbers up to 20 digits requires more than basic division. If the tool tried to divide a 20-digit number by every smaller number, your browser would freeze indefinitely. Instead, this prime number calculator uses a combination of advanced algorithms to ensure speed and accuracy.
The Miller-Rabin Primality Test
To determine if a large number is prime, the tool utilizes the Miller-Rabin primality test. Normally, this is a probabilistic algorithm, meaning it tells you if a number is probably prime. However, by testing a specific, known set of bases (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37), the algorithm becomes completely deterministic (100% accurate) for all 64-bit integers. This allows the tool to instantly verify the primality of numbers up to roughly 18,446,744,073,709,551,615.
Trial Division for Factors
When the Miller-Rabin test identifies a number as composite (not prime), the tool falls back to trial division to find the smallest factor. It divides the input by 2, then by odd numbers up to 1,000,000. If a factor is found, it displays the equation. If the smallest factor is larger than one million, the tool simply confirms the number is not prime without freezing your device.
Sieve of Eratosthenes
When you generate a list of prime numbers, the tool uses the Sieve of Eratosthenes. This ancient and highly efficient algorithm works by creating a grid of numbers and iteratively crossing out the multiples of each prime it finds. It is the fastest way to generate all primes up to a given limit, which is why the tool can instantly output tens of thousands of primes up to 100,000.
Common use cases
Education and Homework
Students learning about fractions, greatest common divisors, and least common multiples frequently need to identify prime numbers. This tool makes it easy to check your work or quickly generate a list of prime numbers up to 100 for reference. If you are working on fraction simplification, you might also find the GCD & LCM Calculator helpful.
Computer Science and Programming
Prime numbers are fundamental to computer science, particularly in hash table sizing and random number generation. Developers often need to find the next prime number larger than a specific power of two. The "Next prime" feature handles this instantly. For broader mathematical operations, you can use the Scientific Calculator or the Number Base Converter.
Cryptography Basics
Modern encryption, such as RSA, relies heavily on the properties of prime numbers. While real-world cryptography uses primes that are hundreds of digits long, a 20-digit prime number checker is perfect for understanding the underlying concepts, testing small-scale implementations, or working through textbook RSA examples.