Introduction
A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. For example, 7 is prime because no other number divides into it evenly. The number 6 is not prime because 2 × 3 = 6.
This prime number calculator lets you check if any number is prime, find the next prime after a number, or find the previous prime before a number. It works with small numbers and very large numbers — up to 1,000 digits long. You can also type math expressions like 2^31-1 or 5!+1, and the calculator will solve them first, then test the result.
For numbers with 15 digits or fewer, the tool tests every possible factor to give you an exact answer. For larger numbers, it uses a fast method called the Miller–Rabin test to determine if a number is almost certainly prime. Every result comes with a step-by-step breakdown so you can see how the answer was found.
How to Use Our Prime Number Calculator
Type a number or math expression and pick what you want to find out. The calculator will tell you if your number is prime, show you the work step by step, and display a chart of nearby primes.
Enter a number or expression: Type a whole number like 97 or a math expression like 2^31-1 into the input box. You can use addition (+), subtraction (-), multiplication (*), division (/), exponents (^), factorials (!), and parentheses. The number can be up to 1,000 digits long.
Action: Use the dropdown menu to choose what you want to do. Pick Check — Is it prime? to test if your number is prime or composite. Pick Find Next Prime to get the first prime number above yours. Pick Find Previous Prime to get the first prime number below yours.
Calculate: Click the Check Number button to run the calculator. Your result will appear below with a clear label, a full list of factors when available, the nearest primes, and a step-by-step breakdown of how the answer was found.
What Is a Prime Number?
A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. For example, 7 is prime because no other number divides into it without a remainder. The number 6 is not prime because 2 × 3 = 6, which means it has extra factors besides 1 and 6.
The First Prime Numbers
The smallest prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Notice that 2 is the only even prime number. Every other even number can be divided by 2, so none of them can be prime. The number 1 is not prime and not composite — it is in a class by itself.
Why Prime Numbers Matter
Every whole number greater than 1 is either prime or can be broken down into a product of primes. For instance, 12 = 2 × 2 × 3. This idea is called the Fundamental Theorem of Arithmetic, and it means prime numbers are the building blocks of all other numbers. They play a key role in computer security, online banking, and encrypted messaging because it is very hard to factor large numbers back into their prime parts.
How to Tell if a Number Is Prime
For small numbers, you can test every whole number from 2 up to the square root of the number. If none of them divide evenly, the number is prime. This method is called trial division. You can use a modulo calculator to check whether one number divides evenly into another. For very large numbers with many digits, trial division takes too long. Instead, mathematicians use fast tests like the Miller–Rabin test, which can say a number is "almost certainly prime" in a fraction of a second. A big number calculator can help you work with integers that have hundreds or even thousands of digits. These tests are not 100% guaranteed, but they are extremely reliable.
Do Prime Numbers Ever End?
No. There are infinitely many prime numbers. The ancient Greek mathematician Euclid proved this over 2,000 years ago. No matter how far you count, there will always be another prime waiting ahead. As numbers get bigger, primes become less common but never stop appearing entirely.