Math

Prime Number Calculator (Is It Prime? Next and Previous Prime)

Enter a whole number to test whether it is prime.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Prime?
Prime?
—
Factorization
—
Next prime
—
Previous prime
—
Gap between them
—

Prime Number Calculator (Is It Prime? Next and Previous Prime) by TheCalcTools

How the Prime Number Calculator (Is It Prime? Next and Previous Prime) works

A prime has exactly two divisors, 1 and itself. The test divides by 2, 3 and every 6k ± 1 up to √n; if none divides evenly, n is prime.

Primes thin out slowly: near n, about one number in ln(n) is prime, so near a million roughly one in 14.

The formula

n is prime if no p ≤ √n divides n

Worked example

Using the default values shown in the calculator:

Whole number1000
  1. 1000 is Composite: 2³ × 5³.
  2. The primes on either side are 997 and 1,009.

Result:

Prime?Composite
Factorization2³ × 5³
Next prime1,009
Previous prime997
Gap between them12

Frequently asked questions

Is 2 the only even prime?

Yes. Every other even number is divisible by 2.

What is the next prime after 1000?

1009. The previous one is 997.

Sources and further reading

Prime Factorization CalculatorEnter a whole number to break it into prime factors Factors Calculator (All Divisors of a Number)Enter a whole number to list all of its factors GCD and LCM CalculatorEnter two whole numbers to find their greatest common divisor and least common multiple Number Base Converter (Binary, Octal, Decimal, Hex)Type a number in any base to see it in binary, octal, decimal and hexadecimal Factorial CalculatorCalculate the factorial n! of a whole number Fibonacci Number CalculatorFind the nth Fibonacci number, where each number is the sum of the two before it

More in Math · All calculators

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.