# Test of primality: is_prime isprime isPrime

### 5.5.14 Test of primality: is_prime isprime isPrime

The is_prime, isprime and isPrime commands are tests for primality.

- is_prime takes one argument:
  n, an integer.
- is_prime(n) returns 1 if n is prime and 0 if n is not prime.

isprime and isPrime are the same as is_prime, except they return true or false.

#### Examples.

- Input:
  is_prime(100003)
  Output:

  1

- Input:
  isprime(100003)
  Output:

  true

- Input:
  is_prime(98569898989987)
  Output:

  1

- Input:
  is_prime(14)
  Output:

  0

- Input:
  isprime(14)
  Output:

  false

You can use the command pari("isprime",n,1) (see Section 5.7.10) to get a primality certificate (see the documentation PARI/GP with the menu Help▸Manuals▸PARI-GP) and pari("isprime",n,2) to use the APRCL test.

#### Examples.

- Input:
  isprime(9856989898997789789)
  Output:

  true

- Input:
  pari("isprime",9856989898997789789,1)
  Output:

  ⎛
  ⎜
  ⎜
  ⎜
  ⎝

  2 | 2 | 1
  19 | 2 | 1
  941 | 2 | 1
  1873 | 2 | 1

  ⎞
  ⎟
  ⎟
  ⎟
  ⎠

  which are the coefficients giving the proof of primality by the p−1 Selfridge-Pocklington-Lehmer test.