Prime Number Checker Calculator

Work out prime number checker instantly with clear inputs, formula shown and shareable results.

About Prime Number Checker Calculator

A prime has exactly two positive divisors: one and itself. Trial division only needs to reach √v, because any factor larger than that pairs with a smaller one already tested.

Formula

Primality by trial division

test divisibility by 2, 3, then 6k ± 1 up to √v

Worked example

With the default values below, Prime Number Checker Calculator returns Result of 9973 is prime. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number to testminimum 1: 9,973
Also test this numberminimum 1: 9,975

Results

Result: 9973 is prime
Smallest prime factor: 9,973
Number of divisors: 2
Second number: 9975 is not prime

Step by step

1Values used
2Primality by trial division
3Result= 9973 is prime
4Smallest prime factor= 9,973
5Number of divisors= 2
6Second number= 9975 is not prime

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is 9973 prime?

Yes — it is the largest four-digit prime.

Why is 1 not prime?

It has only one divisor, and treating it as prime would break the uniqueness of prime factorisation.