Prime Number Checker
Automatically checks whether an integer is prime with reasons. Supports numbers up to 25 digits
Features
Reliably checks numbers up to 25 digits
Accurately determines primality for large integers exceeding 16 digits with no errors
Automatically checks as you type
No execution button needed, displays divisors as the reason
Full-width digits and commas work as-is
Automatically interprets full-width numerals and comma-separated numbers
Copy results as text
Copy the result and reason in 2 lines with a single action
How to Use
Enter the integer to check
Enter a single integer between 0 and 25 digits in the input field
Check the result and reason
The result and reason are automatically displayed as you type
Copy the result if needed
Use the copy button to take the result and reason as 2 lines
Use Cases
Verify homework and classwork
Quickly verify if a number is prime right after solving a problem
Check your own program
Compare the output of your own prime checker program with the result
Check large numbers for primality
Check if 17 to 25-digit integers are prime when a calculator doesn't have enough digits
Play with anniversary numbers
Have fun checking if numbers formed from birthdays or anniversaries are prime
Background
What is a prime number
A prime number is an integer greater than or equal to 2 that has no divisors other than 1 and itself. Numbers like 2, 3, 5, 7, and 11 are prime, and 2 is the only even prime number.
Is 1 a prime number
1 is not a prime number. A prime number is defined as an integer greater than or equal to 2. If 1 were included as a prime, the property that every integer can be expressed uniquely as a product of primes would not hold.
How to identify prime numbers
To determine if an integer n is prime, you can divide it sequentially by numbers up to √n. If it is not divisible by any of them, n is prime. For example, 91 is not prime because it is divisible by 7, which is less than √91 (approximately 9.5).
- Trial division：Trial division is a method that sequentially divides n by numbers from 2 to √n to find divisors. However, the number of divisions becomes enormous as the number of digits increases.
- Miller-Rabin primality test：The Miller-Rabin test checks the remainder of powers using several numbers as bases and finds evidence that a number is not prime. It can determine primality quickly even for large numbers.
Safety and Privacy
Runs entirely in your browser
Your input data is processed only within your browser and is never sent externally.
Processing only in your browser
Calculation of judgment is processed entirely within your browser, and input data is not sent to any server.
Communications encrypted with HTTPS
Page loading is also encrypted by TLS, and content cannot be read by third parties.
No transmission to third parties
Input content is not sent to external services such as ad networks or trackers.
No automatic saving of results
Entered number and input suggestions are not stored on the server.
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Updates
- update #388
Prime number checker added. Determines if integers up to 25 digits are prime, with reasoning
Featured Tools
RAKKOTOOLS is free to use!
Available free of charge for individuals and corporations, commercial and non-commercial use alike.No prior permission or usage application is required. Feel free to use it in various situations.
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We do not guarantee the accuracy or completeness of information and calculation results obtained from each tool.
This notice is a translation of the original Japanese text. If there is any discrepancy between the translation and the original, the Japanese original takes precedence.