Search for a tool
Primality Test

Tool to check if a number is a prime number. A primality test is a mathematical and algorithmic test that indicates whether a number is prime or compound and answers true or false.

Results

Primality Test -

Tag(s) : Arithmetics

Share dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Primality Test tool. Thank you.

# Primality Test

## Prime Number Tester

Tool to check if a number is a prime number. A primality test is a mathematical and algorithmic test that indicates whether a number is prime or compound and answers true or false.

### How to know if a number is a prime?

To know if a number is prime, check if it has any divisor except 1 or itself, this test is called a primality test. The test first uses probabilistic algorithms and if the probability of being prime is non-zero, the algorithms become deterministic (careful verification of potential divisors).

Example: Is 23456789 a prime number ? True
Is 123456789 a prime number ? False

### What are primality tests algorithms?

It exists several test to know if a number is a prime number : Miller–Rabin or Lucas-Lehmer are the one used by dCode.

### Why 1 is not a prime number?

It is mainly a mathematical convention that avoids many problems in mathematical definitions and theorems (where one would have to exclude 1 or treat it as a special case). Another advantage is that the prime factor decomposition is unique 6 = 2*3 and not 1*2*3 or 1*1*1*2*3.

### What is the prime numbers test algorithm?

The deterministic algorithm tries all or almost all numbers (it avoids even numbers and multiples of 3). Here is a pseudo code applicable for prime numbers not too large: // pseudo-code function isprime(n) { if n ≤ 1 return FALSE else if n ≤ 3 return TRUE else if (n mod 2 = 0) or (n mod 3 = 0) return FALSE i = 5 while (i*i ≤ n) { if (n mod i = 0) or (n mod (i + 2) = 0) return FALSE i = i + 6 } return TRUE

## Source code

dCode retains ownership of the source code of the script Primality Test online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Primality Test script for offline use on PC, iPhone or Android, ask for price quote on contact page !