Prime Number Calculator

[ 59 Votes ]

The Prime Number Calculator will:

  1. Confirm if the number is a Prime number or if it is not a Prime number
  2. Calculate any prime number from the smallest to 999999999 (Please note larger numbers may take a few seconds to compute)
  3. Provide a list of numbers that the number can be divided by (note that a Prime number can only be divided by 1 and itself

Prime Number Calculator Parameters: All numbers are integers.

Prime Number Calculator
Prime Number Calculator Results (detailed calculations and formula below)
The multiples of are
is a
Prime Number Calculator Input Values
Number (n) =

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each prime number calculator calculation, the Prime Number Calculator will automatically calculate the results and update the formula elements with each element of the prime number calculator calculation. You can then email or print this prime number calculator calculation as required for later use.

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[ 59 Votes ]

Theoretical description

By definition, prime numbers are those numbers that are divisible only by 1 and by themselves. For example, 3, 5, 7, 11, 13, 17, etc., are all prime numbers as they are divisible only by 1 (3 ÷ 1 = 3; 5 ÷ 1 = 5; 7 ÷ 1 = 7; 11 ÷ 1 = 11; 13 ÷ 1 = 13 and 17 ÷ 1 = 17) and by themselves (3 ÷ 3 = 1; 5 ÷ 5 = 1; 7 ÷ 7 = 1; 11 ÷ 11 = 1; 13 ÷ 13 = 1 and 17 ÷ 17 = 1).

On the other hand, if a number is not prime, then it is composite. By definition, a composite number is a number that is divisible by at least three numbers: by 1, by itself and by another number. For example, 6 is a composite number as besides 1 and 6, it is also divisible by 2 and 3. Obviously, all even numbers except 2 are composite, as all of them are divisible by 2. Moreover, a large deal of odd numbers are also composite, as they are multiples of odd factors (for example, 9 is composite as it is divisible by 3, 15 is also composite as it is divisible by 3 and 5, etc.).

Given the facts above, it is clear that it is not easy to find a general rule that can applied to all numbers to check whether they are prime or composite (in fact, there is yet to be a defined math rule or formula for computing this scenario). You can easily check whether a small number like 39, 59, 67, etc., is prime or composite, but this task becomes complicated when dealing with large numbers, for which divisibility rules are not very helpful, as a number may seem prime but can be a product of two large prime numbers. For example, 13,483 is composite, as it represents the product of 139 × 97, which are both prime. However, you cannot check this through the usual divisibility rules explained in our Arithmetic tutorial on Prime numbers. Therefore, we have provided this prime number calculator so that you can easily check whether a number has other divisors besides 1 and itself or not. In this way, you immediately confirm whether a certain number is prime or composite, therefore saving precious time, which you can use in other operations.

Note for manual calculations to check if a number is a Prime number! Since the square root of a number determines a kind of symmetry, it is not necessary to consider all values from 1 to the given number for all possible divisors. It is sufficient to check from 1 to the square root of that number. For example, to check whether 149 is prime or composite, we must consider the numbers from 1 to 12, as 12 is the closest whole square root to 149 (√144 = 12). Hence, eliminating the even divisors (as 149 is odd) we check whether 149 is prime or composite by dividing it only by 3, 5, 7, 9 and 11. If none of these numbers is a factor of 149, then it is prime (indeed, 149 is actually a prime number).

arithmetic Math Tutorials associated with the Prime Number Calculator

The following Math tutorials are provided within the arithmetic section of our Free Math Tutorials. Each arithmetic tutorial includes detailed arithmetic formula and example of how to calculate and resolve specific arithmetic questions and problems. At the end of each arithmetic tutorial you will find arithmetic revision questions with a hidden answer that reveal when clicked. This allows you to learn about arithmetic and test your knowledge of Math by answering the revision questions on arithmetic.