Prime Number Checker
A prime number is a whole number greater than 1 with exactly two divisors: 1 and itself. Toolverge checks a single number using trial division up to its square root, the standard efficient primality test, and separately lists every prime up to a chosen limit using the sieve of Eratosthenes, a classic algorithm that marks off multiples of each prime it finds. The list is capped at 10,000 to keep the page fast.
Primes up to 50
23571113171923293137414347
How it works
- Enter a number to test whether it is prime.
- Enter a limit to list every prime up to that number (max 10,000).
- Both run instantly in the browser with no backend call.
Formula Trial division up to √n for a single check; sieve of Eratosthenes for a list up to N
Frequently asked questions
Is 17 a prime number?
Yes. 17 has no divisors other than 1 and 17.
Is 1 a prime number?
No. By definition, prime numbers must be greater than 1.
How do you check if a large number is prime?
Test divisibility by every integer from 2 up to the square root of the number; if none divide evenly, it is prime.
What is the sieve of Eratosthenes?
An algorithm that lists all primes up to a limit by marking multiples of each prime it finds as composite, leaving only primes unmarked.
Why is the prime list capped at 10,000?
It keeps the sieve fast and the page responsive; single-number checks have no such limit.