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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.

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Primality Test -

Tag(s) : Arithmetics

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# 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

Example: 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 is_prime(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

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