Primality Test

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

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

dCode can accept numbers up to several hundred of digits, but will stop calculations if the current server load is too high.

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.

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